(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 308876, 7537]*) (*NotebookOutlinePosition[ 309705, 7567]*) (* CellTagsIndexPosition[ 309618, 7561]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Twist2GluonOperator", "Subsection", CellTags->"Twist2GluonOperator"], Cell[CellGroupData[{ Cell["Description", "Subsubsection"], Cell["\<\ Twist2GluonOperator[{p, mu, a}, {nu, b}] or Twist2GluonOperator[p, \ {mu, a}, {nu, b}] or Twist2GluonOperator[p, mu,a, nu,b] yields the 2-gluon \ operator (p is ingoing momentum corresponding to Lorentz index mu). \ Twist2GluonOperator[{p,mu,a}, {q,nu,b}, {k,la,c}] or Twist2GluonOperator[ \ p,mu,a , q,nu,b , k,la,c ] gives the 3-gluon operator. \ Twist2GluonOperator[{p,mu,a}, {q,nu,b}, {k,la,c}, {s,si,d}] or \ Twist2GluonOperator[p,mu,a , q,nu,b , k,la,c , s,si,d] yields the 4-Gluon \ operator. The dimension is determined by the option and Dimension. The \ setting of the option Polarization (unpolarized: 0; polarized: 1) determines \ whether the unpolarized or polarized feynman rule is returned. With the \ setting Explicit to False the color-structure and the (1+(-1)^OPEm) (for \ polarized: (1-(-1)^OPEm)) is extracted and the color indices are omitted in \ the arguments of Twist2GluonOperator.\ \>", "Text"], Cell[TextData[{ "See also: ", " ", ButtonBox["Twist2QuarkOperator", ButtonData:>"Twist2QuarkOperator", ButtonStyle->"Hyperlink", ButtonNote->"Twist2QuarkOperator"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Polarized case, zero-momentum insertion ", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(SetOptions[Twist2GluonOperator, \ Polarization\ -> \ 1, Explicit -> False, \ ZeroMomentumInsertion\ -> \ True]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{CouplingConstant \[Rule] g\_s, Dimension \[Rule] D, Polarization \[Rule] 1, Explicit \[Rule] False, ZeroMomentumInsertion \[Rule] True}\)], "Output"] }, Open ]], Cell["2-gluon legs", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu], a}, {\[Nu], b}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{"\[ImaginaryI]", " ", RowBox[{"(", RowBox[{"1", "-", FormBox[\(\((\(-1\))\)\^m\), "TraditionalForm"]}], ")"}], " ", SubscriptBox["\[Delta]", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}], "G2"], "(", FormBox["p", "TraditionalForm"], ")"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu], a}, {\[Nu], b}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{"\[ImaginaryI]", " ", SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{"1", "-", FormBox[\(\((\(-1\))\)\^m\), "TraditionalForm"]}], ")"}], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(m - 1\)], "TraditionalForm"], " ", SubscriptBox["\[Delta]", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"]}]]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu]}, {\[Nu]}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox["\[Mu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Nu]", "TraditionalForm"]}], "G2"], "(", FormBox["p", "TraditionalForm"], ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu]}, {\[Nu]}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"]}]], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(m - 1\)], "TraditionalForm"]}], TraditionalForm]], "Output"] }, Open ]], Cell["3-gluon legs", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(g\_s\), " ", RowBox[{"(", RowBox[{"1", "-", FormBox[\(\((\(-1\))\)\^m\), "TraditionalForm"]}], ")"}], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]}], "G3"], "(", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["p", "TraditionalForm"], ")"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox["\[Nu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Rho]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Mu]", "TraditionalForm"]}], "G3"], "(", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["p", "TraditionalForm"], ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}]}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(m - 2\)]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], \(m - 2\)]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}], \(m - 2\)]}], "+", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{\(\((\(-1\))\)\^i\), " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{\(\((\(-1\))\)\^i\), " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{\(\((\(-1\))\)\^i\), " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}]}], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]], Cell["4-gluon legs", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}, {s, \[Sigma], d}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ "\[ImaginaryI]", " ", \((1 - \((\(-1\))\)\^m)\), " ", \(g\_s\%2\), " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c112", "TraditionalForm"], "TraditionalForm"]}]]}], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c112", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["d", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}], "G4"], "(", FormBox["p", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], ")"}]}], "-", RowBox[{ SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c112", "TraditionalForm"], "TraditionalForm"]}]], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c112", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["d", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}], "G4"], "(", FormBox["p", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], ")"}]}], "+", RowBox[{ SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c112", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["d", "TraditionalForm"], "TraditionalForm"]}]], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c112", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}], "G4"], "(", FormBox["r", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["p", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}, {s, \[Sigma]}]\ \)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox["\[Mu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Nu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Rho]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Sigma]", "TraditionalForm"]}], "G4"], "(", FormBox["p", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}, {s, \[Sigma]}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(m - 2\)]}], "-", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}]}], "-", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["s", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["s", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}], ")"}], \(\(-i\) + m - 3\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], ")"}], "i"]}]}], HoldForm], "TraditionalForm"], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ FormBox[ TagBox[\(\[Sum]\+\(j = 0\)\%\(m - 4\)\*"\<\"\"\>"\), HoldForm], "TraditionalForm"], "\[NoBreak]", FormBox[\(\[Sum]\+\(i = 0\)\%j\*"\<\"\"\>"\), "TraditionalForm"], "\[NoBreak]", FormBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(\(-j\) + m - 4\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], "-", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(j - i\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}], ")"}]}], ")"}], "i"]}], "TraditionalForm"]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["\[Epsilon]", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"], "\[NoBreak]", FormBox["s", "TraditionalForm"]}]]}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["s", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ FormBox[ TagBox[\(\[Sum]\+\(j = 0\)\%\(m - 4\)\*"\<\"\"\>"\), HoldForm], "TraditionalForm"], "\[NoBreak]", FormBox[\(\[Sum]\+\(i = 0\)\%j\*"\<\"\"\>"\), "TraditionalForm"], "\[NoBreak]", FormBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], \(\(-j\) + m - 4\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], "-", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(j - i\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}], ")"}]}], ")"}], "i"]}], "TraditionalForm"]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["\[Epsilon]", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"], "\[NoBreak]", FormBox["s", "TraditionalForm"]}]]}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["s", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ FormBox[ TagBox[\(\[Sum]\+\(j = 0\)\%\(m - 4\)\*"\<\"\"\>"\), HoldForm], "TraditionalForm"], "\[NoBreak]", FormBox[\(\[Sum]\+\(i = 0\)\%j\*"\<\"\"\>"\), "TraditionalForm"], "\[NoBreak]", FormBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(\(-j\) + m - 4\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], "-", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(j - i\)]}], "TraditionalForm"]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["\[Epsilon]", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]]}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["p", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{ FormBox[ TagBox[\(\[Sum]\+\(j = 0\)\%\(m - 4\)\*"\<\"\"\>"\), HoldForm], "TraditionalForm"], "\[NoBreak]", FormBox[\(\[Sum]\+\(i = 0\)\%j\*"\<\"\"\>"\), "TraditionalForm"], "\[NoBreak]", FormBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], \(\(-j\) + m - 4\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], "-", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(j - i\)]}], "TraditionalForm"]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["\[Epsilon]", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"], "\[NoBreak]", FormBox["r", "TraditionalForm"]}]]}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["\[Epsilon]", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", FormBox["q", "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}]}], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Unpolarized case, zero-momentum insertion", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(SetOptions[Twist2GluonOperator, Polarization \[Rule] 0, ZeroMomentumInsertion \[Rule] True]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{CouplingConstant \[Rule] g\_s, Dimension \[Rule] D, Polarization \[Rule] 0, Explicit \[Rule] False, ZeroMomentumInsertion \[Rule] True}\)], "Output"] }, Open ]], Cell["2-gluon legs", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu], a}, {\[Nu], b}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(1\/2\), " ", RowBox[{"(", RowBox[{ FormBox[\(\((\(-1\))\)\^m\), "TraditionalForm"], "+", "1"}], ")"}], " ", SubscriptBox["\[Delta]", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}], "G2"], "(", FormBox["p", "TraditionalForm"], ")"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu], a}, {\[Nu], b}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(1\/2\), " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ FormBox[\(\((\(-1\))\)\^m\), "TraditionalForm"], "+", "1"}], ")"}], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(m - 2\)], "TraditionalForm"], " ", SubscriptBox["\[Delta]", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"]}]]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu]}, {\[Nu]}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox["\[Mu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Nu]", "TraditionalForm"]}], "G2"], "(", FormBox["p", "TraditionalForm"], ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[p, {\[Mu]}, {\[Nu]}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ RowBox[{"(", FormBox[ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], "TraditionalForm"], ")"}], "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], "2"]}]}], ")"}], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(m - 2\)], "TraditionalForm"]}], TraditionalForm]], "Output"] }, Open ]], Cell["3-gluon legs", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(-\(1\/2\)\), " ", "\[ImaginaryI]", " ", \(g\_s\), " ", RowBox[{"(", RowBox[{ FormBox[\(\((\(-1\))\)\^m\), "TraditionalForm"], "+", "1"}], ")"}], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]}], "G3"], "(", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["p", "TraditionalForm"], ")"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox["\[Nu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Rho]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Mu]", "TraditionalForm"]}], "G3"], "(", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["p", "TraditionalForm"], ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["q", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["p", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}]}], ")"}], "i"]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["r", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["p", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["r", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}], "+", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["q", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["q", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}]}], ")"}], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}], \(m - 2\)], "TraditionalForm"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["q", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["q", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]]}]}], ")"}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}]}]}], ")"}], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}], \(m - 2\)], "TraditionalForm"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["r", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["r", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}]}]}], ")"}], " ", FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], ")"}], \(m - 2\)], "TraditionalForm"]}]}], TraditionalForm]], "Output"] }, Open ]], Cell["4-gluon legs", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}, {s, \[Sigma], d}]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(1\/2\), " ", \((1 + \((\(-1\))\)\^m)\), " ", \(g\_s\%2\), " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c113", "TraditionalForm"], "TraditionalForm"]}]]}], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c113", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["d", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}], "G4"], "(", FormBox["p", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], ")"}]}], "-", RowBox[{ SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c113", "TraditionalForm"], "TraditionalForm"]}]], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c113", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["d", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}], "G4"], "(", FormBox["p", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], ")"}]}], "+", RowBox[{ SubscriptBox["f", RowBox[{ FormBox[ FormBox["a", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c113", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["d", "TraditionalForm"], "TraditionalForm"]}]], " ", SubscriptBox["f", RowBox[{ FormBox[ FormBox["b", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["c113", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{"(", RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[VeryThinSpace]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}], "G4"], "(", FormBox["r", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["p", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}, {s, \[Sigma]}]\ \)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["O", RowBox[{ FormBox["\[Mu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Nu]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Rho]", "TraditionalForm"], "\[VeryThinSpace]", FormBox["\[Sigma]", "TraditionalForm"]}], "G4"], "(", FormBox["p", "TraditionalForm"], ",", FormBox["q", "TraditionalForm"], ",", FormBox["r", "TraditionalForm"], ",", FormBox["s", "TraditionalForm"], ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Twist2GluonOperator[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}, {s, \[Sigma]}, Explicit -> True]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(m - 2\)]}], "+", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["p", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]}]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["p", "TraditionalForm"]}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"(", FormBox[ TagBox[ RowBox[{\(\[Sum]\+\(i = 0\)\%\(m - 3\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", RowBox[{"(", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], ")"}]}], ")"}], "i"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["r", "TraditionalForm"]}], "+", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["s", "TraditionalForm"]}]}], ")"}], \(\(-i\) + m - 3\)]}]}], HoldForm], "TraditionalForm"], ")"}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Mu]", "TraditionalForm"], "TraditionalForm"]], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["q", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox["g", RowBox[{ FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"], "\[NoBreak]", FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]}]], " ", RowBox[{ FormBox["\[CapitalDelta]", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox["q", "TraditionalForm"]}], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "-", RowBox[{ SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Nu]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["\[CapitalDelta]", "TraditionalForm"], FormBox[ FormBox["\[Rho]", "TraditionalForm"], "TraditionalForm"]], " ", SuperscriptBox[ FormBox["q", "TraditionalForm"], FormBox[ FormBox["\[Sigma]", "TraditionalForm"], "TraditionalForm"]]}], "+", RowBox[{