(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 57689, 1547] NotebookOptionsPosition[ 54545, 1444] NotebookOutlinePosition[ 54945, 1461] CellTagsIndexPosition[ 54902, 1458] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "STellipse-", StyleBox["Mathematica", FontSlant->"Italic"], " Implementation" }], "Title", CellChangeTimes->{{3.486739102742792*^9, 3.486739106582312*^9}, { 3.48674195091687*^9, 3.486741982018971*^9}}], Cell[TextData[{ "R. Michael Winters, Deva O'Neil, College of Wooster NSF-REU, June 2010. \ Updated 10/1/2011.\n", StyleBox["MikeWinters10@gmail.com, DONeil@bridgewater.edu", FontSlant->"Italic"] }], "Text", CellChangeTimes->{{3.486737803190709*^9, 3.486737870690131*^9}, { 3.486741680047111*^9, 3.4867418046064672`*^9}, {3.52303449451597*^9, 3.5230344997964983`*^9}, {3.5264797710228357`*^9, 3.5264797768728356`*^9}}], Cell[CellGroupData[{ Cell["Generating Ellipses in Mathematica", "Subtitle", CellChangeTimes->{{3.48518704915347*^9, 3.48518709941292*^9}, { 3.486733030085766*^9, 3.4867330356263847`*^9}}], Cell[TextData[{ "The following file was generated as a means to generate ellipses for the \ oblique parameters in ", StyleBox["Mathematica ", FontSlant->"Italic"], "and was modeled on the OPUCEM folder ", StyleBox["https://projects.hepforge.org/opucem/trac/browser/tags/opucem-00-\ 00-03/tools/STellipse/drawEll.H.", FontSlant->"Italic"], " It may also be useful to users who wish to create ellispes without using \ ROOT. We are using values for S, T, sigS, sigT, and \[Rho] as defined in the \ \"NEW results (summer 09)\" section of OPUCEM's 'drawST.C' file." }], "Subsubtitle", CellChangeTimes->{{3.4852746720902863`*^9, 3.4852747154711018`*^9}, { 3.485274914164317*^9, 3.485274997988399*^9}, {3.485275316208455*^9, 3.485275359387558*^9}, {3.485515560781208*^9, 3.48551559110069*^9}, { 3.486477020639594*^9, 3.486477048866544*^9}, {3.486732794845839*^9, 3.4867328115541553`*^9}, {3.4867330510112753`*^9, 3.486733299193038*^9}, { 3.486733353061388*^9, 3.4867334247384377`*^9}, {3.486733972171994*^9, 3.486733976205003*^9}, {3.486734319100408*^9, 3.486734361448554*^9}, { 3.486734722676229*^9, 3.486734724618517*^9}, {3.4867394967838573`*^9, 3.486739576112936*^9}, {3.486739624923201*^9, 3.4867396357146*^9}, { 3.48674200257762*^9, 3.486742006713024*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.485520682325533*^9, 3.485520694881955*^9}, { 3.486734516041684*^9, 3.4867345215673723`*^9}, {3.4867396605786753`*^9, 3.486739667512991*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "First ", Cell[BoxData[ FormBox[ SuperscriptBox["\[CapitalDelta]\[Chi]", "2"], TraditionalForm]], "None"] }], "Subsection", CellChangeTimes->{{3.485515604453515*^9, 3.485515614928668*^9}}], Cell[TextData[{ "We are given 6 values to construct our ellipse. Though S and T represent \ the center of the ellipse, sigS and sigT represent the 1 sigma uncertainties, \ not the values for the major and minor axes ", StyleBox["a", FontSlant->"Italic"], " and ", StyleBox["b", FontSlant->"Italic"], ". Furthermore, \[Rho] is the correlation coefficeint used to calculate \ the angle of rotation \[Alpha]. We use ", Cell[BoxData[ FormBox[ SubscriptBox["\[Chi]", "sq"], TraditionalForm]]], " to represent ", Cell[BoxData[ FormBox[ SuperscriptBox["\[CapitalDelta]\[Chi]", "2"], TraditionalForm]]], ". " }], "Text", CellChangeTimes->{{3.485515667721374*^9, 3.485515756769354*^9}, { 3.485601594105598*^9, 3.485601617103196*^9}, {3.4856023510707912`*^9, 3.485602368925871*^9}, 3.485602407610777*^9, {3.486732826411231*^9, 3.486732826649397*^9}, {3.486733346807434*^9, 3.486733346965481*^9}, { 3.4867347429917517`*^9, 3.486734760934907*^9}, 3.4867349594665003`*^9, { 3.486738774247158*^9, 3.48673877446947*^9}, {3.486739700910581*^9, 3.486739767801876*^9}, {3.486741865148346*^9, 3.486741889433515*^9}, { 3.4867419343988047`*^9, 3.4867419370784473`*^9}}], Cell[TextData[{ "These values of S and T correspond to ", Cell[BoxData[ FormBox[ SubscriptBox["m", "h"], TraditionalForm]], FormatType->"TraditionalForm"], "=150 GeV and ", Cell[BoxData[ FormBox[ SubscriptBox["m", "t"], TraditionalForm]], FormatType->"TraditionalForm"], "=175 GeV. (See 'drawST.C')" }], "Text", CellChangeTimes->{{3.4867414363054533`*^9, 3.4867414751672773`*^9}, { 3.486741641697589*^9, 3.486741658280744*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Sbaseline", " ", "=", " ", ".05"}], ";", " ", RowBox[{"Tbaseline", " ", "=", " ", ".10"}], ";"}], " "}]], "Input"], Cell[TextData[{ "These baseline values are shifted to correspond to ", Cell[BoxData[ FormBox[ SubscriptBox["m", "h"], TraditionalForm]], FormatType->"TraditionalForm"], "=115 GeV and ", Cell[BoxData[ FormBox[ SubscriptBox["m", "t"], TraditionalForm]], FormatType->"TraditionalForm"], "=173.1 GeV. 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Cowan. This article \ can be found at ", StyleBox["http://pdg.lbl.gov/2009/reviews/rpp2009-rev-statistics.pdf", FontSlant->"Italic"], ". 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Because this system of \ equations will yield a set of 4 solutions (\[PlusMinus]a, \[PlusMinus]b), we \ choose the first set and define ", StyleBox["a", FontSlant->"Italic"], " and ", StyleBox["b", FontSlant->"Italic"], " as the absolute value of the answers. 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The comparison to the 'draw.H' formulation is displayed in the \ section entitled \"Verifying the drawEll.H code.\" " }], "Text", CellChangeTimes->{{3.485601446633285*^9, 3.485601481407216*^9}, { 3.486477340742651*^9, 3.486477434640458*^9}, {3.4867341543592463`*^9, 3.486734273958476*^9}, {3.486734461074333*^9, 3.486734469858943*^9}, { 3.48673487480646*^9, 3.4867348876301928`*^9}, {3.486738813771134*^9, 3.486738819498407*^9}, {3.486740476193583*^9, 3.48674048060881*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Second ", Cell[BoxData[ FormBox[ SuperscriptBox["\[CapitalDelta]\[Chi]", "2"], TraditionalForm]], "None"] }], "Subsection", CellChangeTimes->{{3.485515978277857*^9, 3.485515985752479*^9}}], Cell[TextData[{ "This is our second value for ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["\[CapitalDelta]\[Chi]", "2"], "."}], TraditionalForm]]], " It generates the 2 sigma ellipse without changing any of the other inputs. \ We are using the same command sequence but defining 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