GIFSchool: phenHiggs.nb

(************** Content-type: application/mathematica **************

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Notebook[{

Cell[CellGroupData[{
Cell["Phenomenology of pp\[Rule]H+X at NLO", "Subtitle"],

Cell[CellGroupData[{

Cell["Introduction", "Section"],

Cell[TextData[{
  StyleBox["In this notebook we calculate the inclusive cross section for \
Higgs production at hadron colliders, at NLO in the strong coupling. We use \
the analytic results obtained in a previous notebook corresponding to the \
original calculation by Sally Dawson (Nuclear Physics B (1991) 283). To get \
useful numbers we use a modern set of PDF, i.e. the MRST as implemented in ",
    FontSize->16],
  StyleBox["Mathematica",
    FontSize->16,
    FontSlant->"Italic"],
  StyleBox[" by J.Andersen (many thanks!).  A description of the calculation, \
including the formulas used here for the numerical results, is given in the \
notes.",
    FontSize->16]
}], "Text"]
}, Closed]],

Cell[CellGroupData[{

Cell["Preliminaries", "Section"],

Cell["\<\
Off[General::spell];
Off[General::spell1];
Clear[\"Global`*\"];\
\>", "Input"],

Cell[CellGroupData[{

Cell["Install Vegas", "Subsection"],

Cell["\<\
I use the  Vegas package of CUBA library of T. Hahn \
(hep-ph/0404043). If you do not want to use it, use NIntegrate instead of \
Vegas\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Install["\</Users/fabiomaltoni/Physics/Codes/CUBA/VegasX\>"] 
      Install["\</Users/fabiomaltoni/Physics/Codes/CUBA/SuaveX\>"]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`LinkObject[
        "/Users/fabiomaltoni/Physics/Codes/CUBA/SuaveX", 3, 3]\ LinkObject[
        "/Users/fabiomaltoni/Physics/Codes/CUBA/VegasX", 2, 2]\)], "Output"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Call special graphics routines", "Subsection"],

Cell["\<\
<< Graphics`Colors`;
<< Graphics`Graphics`;\
\>", "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["Install PDF'S: for help read the PDF-HOWTO document", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(SetDirectory["\<~/Physics/Teaching/pp>Higgs\ at\ NLO/Jeppe\>"]\), "\
\[IndentingNewLine]", 
    \(Install["\<pdf.exe\>"]\)}], "Input"],

Cell[BoxData[
    \(TraditionalForm\`"/Users/fabiomaltoni/Physics/Teaching/pp>Higgs at \
NLO/Jeppe"\)], "Output"],

Cell[BoxData[
    \(TraditionalForm\`LinkObject["./pdf.exe", 4, 4]\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\

<<\"loadCTEQ5.m\";\
\>", "Input"],

Cell[BoxData[
    \(TraditionalForm\`"Loading Package: PDF"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"PDF's from CTEQ5"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"Eur.Phys.J.C12:375-392,2000 "\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"*** Warning *** Unofficial release. "\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"*** Cross-check with official Fortran code."\)], \
"Print"],

Cell[BoxData[
    \(TraditionalForm\`" Version 1.0: Written by Tamara Trout & Fred Olness, \
October 1, 2000"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`" "\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"In case of problems, contact:"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"Fred Olness: olness@mail.physics.smu.edu"\)], "Print"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Wrapper to call the pdf. Notation is self-explanatory. Just notice \
that all parton distribution codes usually return x f(x). To avoid confusion, \
at expense of a couple more floating point operations, I divide all the \
values by the corresponding x.  pdfcall calculates the parton-parton \
luminoties, gg qg, qq~\
\>", "Subsubsection"],

Cell["\<\
(* MRST *)

pdfMRST[X1_,X2_,q_]:=Module[
{Q,xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF,pd1,pd2,xgg,xqg,xqq},
Q=q*1.;
xgDF =f[3,X1,Q]/X1;
xdbDF=f[8,X1,Q]/X1;
xdDF =f[2,X1,Q]/X1+xdbDF;
xubDF=f[4,X1,Q]/X1;
xuDF =f[1,X1,Q]/X1+xubDF;
xsDF =f[6,X1,Q]/X1;
xcDF =f[5,X1,Q]/X1;
xbDF =f[7,X1,Q]/X1;

pd1={xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF};
xgDF =f[3,X2,Q]/X2;
xdbDF=f[8,X2,Q]/X2;
xdDF =f[2,X2,Q]/X2+xdbDF;
xubDF=f[4,X2,Q]/X2;
xuDF =f[1,X2,Q]/X2+xubDF;
xsDF =f[6,X2,Q]/X2;
xcDF =f[5,X2,Q]/X2;
xbDF =f[7,X2,Q]/X2;
pd2={xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF};


xgg=pd1[[1]]*pd2[[1]];
xqg=pd1[[1]]*(pd2[[2]]+pd2[[3]]+pd2[[4]]+pd2[[5]]+2(pd2[[6]]+pd2[[7]]+pd2[[8]]\
))+
   pd2[[1]]*(pd1[[2]]+pd1[[3]]+pd1[[4]]+pd1[[5]]+2(pd1[[6]]+pd1[[7]]+pd1[[8]])\
);
xqq=pd1[[2]]*pd2[[3]]+pd1[[4]]*pd2[[5]]+pd1[[3]]*pd2[[2]]+pd1[[5]]*pd2[[4]]+
   2(pd1[[6]] pd2[[6]]+pd1[[7]] pd2[[7]]+pd1[[8]] pd2[[8]]);
  
  Return[{xgg,xqg,xqq}]; 
];\
\>", "Input"],

Cell["\<\

(* cteq5 *)\
\>", "Input"],

Cell["\<\
pdfCTEQ[X1_,X2_,q_]:=Module[
{Q,pd1,pd2,xgg,xqg,xqq},
Q=q*1.;

pd1={cteq5pdf[1,0,X1,Q],
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     cteq5pdf[1,-1,X1,Q],
     cteq5pdf[1,3,X1,Q],
     cteq5pdf[1,4,X1,Q],
     cteq5pdf[1,5,X1,Q]};
pd2={cteq5pdf[1,0,X2,Q],
     cteq5pdf[1,2,X2,Q],
     cteq5pdf[1,-2,X2,Q],
     cteq5pdf[1,1,X2,Q],
     cteq5pdf[1,-1,X2,Q],
     cteq5pdf[1,3,X2,Q],
     cteq5pdf[1,4,X2,Q],
     cteq5pdf[1,5,X2,Q]};
     
xgg=pd1[[1]]*pd2[[1]];
xqg=pd1[[1]]*(pd2[[2]]+pd2[[3]]+pd2[[4]]+pd2[[5]]+2(pd2[[6]]+pd2[[7]]+pd2[[8]]\
))+
   pd2[[1]]*(pd1[[2]]+pd1[[3]]+pd1[[4]]+pd1[[5]]+2(pd1[[6]]+pd1[[7]]+pd1[[8]])\
);
xqq=pd1[[2]]*pd2[[3]]+pd1[[4]]*pd2[[5]]+pd1[[3]]*pd2[[2]]+pd1[[5]]*pd2[[4]]+
   2(pd1[[6]] pd2[[6]]+pd1[[7]] pd2[[7]]+pd1[[8]] pd2[[8]]);
  
  Return[{xgg,xqg,xqq}]; 
];

pdfCTEQLO[X1_,X2_,q_]:=Module[
{Q,xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF,pd1,pd2,xgg,xqg,xqq},
Q=q*1.;

pd1={cteq5pdf[3,0,X1,Q],
     cteq5pdf[3,2,X1,Q],
     cteq5pdf[3,-2,X1,Q],
     cteq5pdf[3,1,X1,Q],
     cteq5pdf[3,-1,X1,Q],
     cteq5pdf[3,3,X1,Q],
     cteq5pdf[3,4,X1,Q],
     cteq5pdf[3,5,X1,Q]};
pd2={cteq5pdf[3,0,X2,Q],
     cteq5pdf[3,2,X2,Q],
     cteq5pdf[3,-2,X2,Q],
     cteq5pdf[3,1,X2,Q],
     cteq5pdf[3,-1,X2,Q],
     cteq5pdf[3,3,X2,Q],
     cteq5pdf[3,4,X2,Q],
     cteq5pdf[3,5,X2,Q]};
     
xgg=pd1[[1]]*pd2[[1]];
xqg=pd1[[1]]*(pd2[[2]]+pd2[[3]]+pd2[[4]]+pd2[[5]]+2(pd2[[6]]+pd2[[7]]+pd2[[8]]\
))+
   pd2[[1]]*(pd1[[2]]+pd1[[3]]+pd1[[4]]+pd1[[5]]+2(pd1[[6]]+pd1[[7]]+pd1[[8]])\
);
xqq=pd1[[2]]*pd2[[3]]+pd1[[4]]*pd2[[5]]+pd1[[3]]*pd2[[2]]+pd1[[5]]*pd2[[4]]+
   2(pd1[[6]] pd2[[6]]+pd1[[7]] pd2[[7]]+pd1[[8]] pd2[[8]]);
  
  Return[{xgg,xqg,xqq}]; 
];\
\>", "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Decide the pdf family to be used ", "Subsubsection"],

Cell["pdfcall[x__] = pdfCTEQ[x];", "Input"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Alpha_S: Very basic implementation of Alpha_S. 
Check that the value of Lamda_4 or Lambda_5 is consistent with that of the \
PDF. 
One simple, but indirect way to do it is to compare the value of alphas(MZ) \
with the one quoted by MRST.\
\>", "Subsection"],

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\ \ \ \), "\[IndentingNewLine]", 
    \(\(bp[
          nf_] := \(\(\((153 - 19\ nf)\)/2\)/
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    \(\(\(mb = 4.75;\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]", 
    \(\(\[CapitalLambda][5] = 0.146;\)\), "\[IndentingNewLine]", 
    \(\(asLO[q_, nf_] = 1/\((b[nf]\ t[nf])\);\)\), "\n", 
    \(\(\[CapitalLambda][5] = 0.226;\)\), "\[IndentingNewLine]", 
    \(\(asNLO[q_, nf_] = 
        1/\((b[nf]\ t[nf])\) \((1 - 
              bp[nf]/b[nf]\ Log[t[nf]]/t[nf])\);\)\)}], "Input"],

Cell[CellGroupData[{

Cell["\<\
Check the values of alpha_S at the scale MZ\
\>", "Subsubsection"],

Cell[CellGroupData[{

Cell["asNLO[91.118,5]", "Input"],

Cell[BoxData[
    \(TraditionalForm\`0.11799518835498905`\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Color factors ", "Subsection"],

Cell["\<\
CF=4/3;
CA=3;
nf=5;
TF=1/2;
b0=11/6 CA -2 nf TF/3;
\
\>", "Input"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["LO cross section", "Section"],

Cell[CellGroupData[{

Cell["\<\
Integral of the LO loop. The sign of the Imaginary part is given by \
the usual prescription mt^2-i eps which is equivalent to t+i eps in the \
notation below.
t=mh^2/4/mt^2;\
\>", "Subsubsection"],

Cell[" ", "Input"],

Cell[CellGroupData[{

Cell["\<\
eps=0.00000001;
inte[t_]=3*Integrate[(1-4 x y)/(1-4 t x y),{x,0,1},{y,0,1-x}]//Simplify;
Plot[{Re[inte[t+I eps]],Im[inte[t+I \
eps]]},{t,0,10},PlotStyle\[Rule]{{Blue,Thickness[0.007]},{Red,Thickness[0.007]\
}}];\
\>", "Input"],

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ool0003oooooo`00000:ooooo`03o`000?oooooooooo0?ooooooV?ooool000;ooooo00?o0000oooo
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oiSooooo000Mooooo`03o`000?oooooooooo0?ooooooV?ooool00?oooooo^?ooool00001\
\>"],
  ImageRangeCache->{{{0, 438.375}, {270.562, 0}} -> {-0.732569, -0.112555, \
0.025053, 0.00704711}}]
}, Open  ]],

Cell["\<\
Plot of the real and imaginary part of 3*I(a) as defined in the \
notes (I use 3*I(a) so that the function goes to 1 as a->0.)\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
  "Function to be integrated to get the LO cross section. In general, we use \
the convention that all functions to be numerically integrated in the \
hypercubes ",
  Cell[BoxData[
      \(TraditionalForm\`\([0, 1]\)\^d\)]],
  ", where d is the dimension of the integration space. dsigma depends on the \
Higgs mass (mh), the total collider energy (sqrtS) and from the arbitrary \
normalization and factorization scales (mur,muf)."
}], "Subsubsection"],

Cell["\<\
dsigmaLO[zz_,mh_,sqrtS_,muf_,mur_]:=Module[
{y,x1,x2,gg0,qg0,qq0,s0,ymin,ymax,JAC,v,S,tau0},
Muf=muf*1.;
v=246.;
S=sqrtS^2;
tau0=mh^2/S;
ymax=-Log[Sqrt[tau0]];
ymin=-ymax;
y=ymin+(ymax-ymin)*zz;
JAC=ymax-ymin;
x1=Sqrt[tau0] Exp[y];
x2=Sqrt[tau0] Exp[-y];
{gg0,qg0,qq0}=pdfCTEQLO[x1,x2,Muf];
s0=asLO[mur,5]^2/576/Pi/v^2*tau0;
s0=s0*gg0;
s0=s0*389379660; (*to picobarns*)
s0=s0*JAC;
Return[s0];
];\
\>", "Input"],

Cell[CellGroupData[{

Cell["sLO=NIntegrate[dsigmaLO[xx,100,14000,100,100],{xx,0,1}]", "Input"],

Cell[BoxData[
    \(TraditionalForm\`28.056643821030747`\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
Get the cross section for various Higgs masses and including the \
form factor of the loop.
I first build a table with the results of the cross section in picobarns, and \
then plot it.\
\>", "Subsection"],

Cell["\<\
resEFT=Table[{i,NIntegrate[dsigmaLO[x,i*1.,14000.,i*1.,i*1.],{x,0,1}\
]},{i,20,600,10}];\
\>", "Input"],

Cell["\<\
resFULL=Table[{resEFT[[i]][[1]],Abs[inte[resEFT[[i]][[1]]^2/175^2/4]\
]^2*resEFT[[i]][[2]]},{i,1,Length[resEFT]}];\
\>", "Input"],

Cell["resFULL", "Input"],

Cell[CellGroupData[{

Cell[TextData[{
  "Show[LogListPlot[resEFT, ",
  StyleBox["PlotJoined", "MR"],
  " ",
  StyleBox["->", "MR"],
  " ",
  StyleBox["True,", "MR"],
  "PlotStyle\[Rule]{Red}],\nplotFULL=LogListPlot[resFULL, ",
  StyleBox["PlotJoined", "MR"],
  " ",
  StyleBox["->True,", "MR"],
  "PlotStyle\[Rule]{Blue}]];\n\n"
}], "Input"],

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\>"],
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Cell["\<\
Cross section (pb) as a function of the Higgs mass. This plot shows \
how well the EFT does. For a Higgs<200 GeV the approximation is very \
good.\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Various ways to do the integration over the x1 and x2.", "Subsection"],

Cell[CellGroupData[{

Cell["\<\

uno=Integrate[x1*x2,{x1,t0,1},{x2,t0/x1,1}]//Expand
due=Integrate[ta,{ta,t0,1},{y,Log[Sqrt[ta]],-Log[Sqrt[ta]]}]//PowerExpand//\
Expand
tre=Integrate[t0/z \
t0/z^2,{z,t0,1},{y,Log[Sqrt[t0/z]],-Log[Sqrt[t0/z]]}]//PowerExpand//Expand\
\>\
", "Input"],

Cell[BoxData[
    \(TraditionalForm\`1\/2\ \(log(t0)\)\ t0\^2 - t0\^2\/4 + 1\/4\)], "Output"],

Cell[BoxData[
    \(TraditionalForm\`1\/2\ \(log(t0)\)\ t0\^2 - t0\^2\/4 + 1\/4\)], "Output"],

Cell[BoxData[
    \(TraditionalForm\`1\/2\ \(log(t0)\)\ t0\^2 - t0\^2\/4 + 1\/4\)], "Output"]
}, Open  ]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["NLO cross section", "Section"],

Cell["\<\
We have integrate over the angular variables, so we are only left \
with two integrations. One is over z (=mh/S/x1/x2) and the other over the \
rapidity y of the partonic cms. For every point in the phase space we have to \
calculate an event and a corresponding counter-event with z=1 to implement \
the + distributions in the gg channel. Various contributions add to the final \
result:

virtual: gg>h  at 1-loop + corrections to the effective lagrangian (UV and IR \
divergent)
real: qq~ >h g (finite)
           qg > qh (collinear divergent)
            gg>gh  (soft and collinear divergent)
\
\>", "Text",
  FontSize->16],

Cell[CellGroupData[{

Cell["Born+Virtual ", "Subsection"],

Cell[TextData[{
  "dsigmaBV[yy_,mh_,sqrtS_,muf_,mur_]:=Module[\n",
  StyleBox["(* local variables *)",
    FontColor->RGBColor[0, 1, 0]],
  "\n{y0,x10,x20,sig0,ymax0,JAC0,v,S,tau0,beta,gg0,qg0,qq0},\nMuf=muf 1.;\n\
Mur=mur 1.;\nv=246.;\nS=sqrtS^2;\ntau0=mh^2/S;\nbeta=Sqrt[1-tau0];\n\n",
  StyleBox["(* calculate quantities for z=1 *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nymax0=-Log[Sqrt[tau0]];\ny0=-ymax0+2*ymax0*yy;\nJAC0=2*ymax0;\n\
x10=Sqrt[tau0] Exp[y0];\nx20=Sqrt[tau0] Exp[-y0];\n\
{gg0,qg0,qq0}=pdfcall[x10,x20,Muf];\n\n",
  StyleBox["(* sigma0 *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nsig0=asNLO[Mur,5]^2/576/Pi/v^2*tau0;\nsig0=sig0+sig0*asNLO[Mur,5]/2/Pi*\n\
(11/3 CA+ 2 Pi^2 - 2 b0 2 Log[Muf/Mur]+\n16 CA Log[beta] Log[mh/Muf]+16 CA \
Log[beta]^2);\nsig0=sig0*gg0;\nsig0=sig0*389379660; (*to picobarns*)\n\
sig0=sig0*JAC0;\n\n\
(*Print[{muf,mur,v,S,tau0,beta,ymax0,y0,JAC0,x10,x20,gg0,qg0,qq0,sig0}];*)\n\
Return[sig0];\n];"
}], "Input"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Real contributions", "Subsection"],

Cell[TextData[{
  "dsigmaR[xx_,yy_,mh_,sqrtS_,muf_,mur_]:=Module[\n",
  StyleBox["(* local variables *)",
    FontColor->RGBColor[0, 1, 0]],
  "\n{v,S,tau0,\n y,y0,z,tau,\n x1,x2,x10,x20,\n ymax0,ymax,\n JAC,JAC0,\n \
gg,qg,qq,gg0,qg0,qq0,\n qqterm,qgterm,ggterm,ggterm0,\n sig,sig0,\n Muf},\n\n\
v=246.;\nS=sqrtS^2;\ntau0=mh^2/S;\nMuf=muf*1.0;\n\n",
  StyleBox["(* calculate quantities for an event *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nz=tau0+(1-tau0)*xx;\ntau=tau0/z;\nymax =-Log[Sqrt[tau]];\n\
y=-ymax+2*ymax*yy;\nJAC =2*ymax*(1-tau0)*tau0/z^2;\nx1=Sqrt[tau] Exp[y];\n\
x2=tau/x1;\n",
  StyleBox["(* call the pdf *)\n",
    FontColor->RGBColor[1, 0, 0]],
  "\n{gg,qg,qq}=pdfcall[x1,x2,Muf];\n\n",
  StyleBox["(* calculate quantities for counter-event *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nymax0=-Log[Sqrt[tau0]];\ny0=-ymax0+2*ymax0*yy;\n\
JAC0=2*ymax0*(1-tau0)*tau0;\nx10=Sqrt[tau0] Exp[y0];\nx20=tau0/x10;\n",
  StyleBox["(* call the pdf at z=1 *)",
    FontColor->RGBColor[1, 0, 0]],
  "\n{gg0,qg0,qq0}=pdfcall[x10,x20,Muf];\n\n",
  StyleBox["(* sigma0 *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nsig0=asNLO[mur,5]^2/576/Pi/v^2;\nsig0=sig0*asNLO[mur,5]/2/Pi;\n\n",
  StyleBox["(* qq channnel : no counter event *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nqqterm=64/27*(1-z)^3;\nqqterm=qqterm*sig0*JAC*qq;\n\n",
  StyleBox["(* qg channnel : no counter event *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nqgterm=CF*( (1+(1-z)^2)/z (2*Log[mh/muf]+2 Log[1-z]-Log[z])\n           \
+(z^2-3/2(1-z)^2)/z )*z;\nqgterm=qgterm*sig0*JAC*qg;\n\n",
  StyleBox["(* gg channnel *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nggterm=CA*(2 (2 (z/(1-z)+(1-z)/z+z (1-z) )) * (2*Log[mh/muf])-\n       \
11/3 (1-z)^3/z -\n       4 (1-z+z^2)^2/z/(1-z) Log[z]+\n       8 \
(1-z+z^2)^2/z Log[1-z]/(1-z) )*z;\nggterm=ggterm*sig0*JAC*gg;\n",
  StyleBox["(* gg counter-event *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nggterm0=CA*(-4/(1-z) 2*Log[mh/muf] - 8*Log[1-z]/(1-z) );\n\
ggterm0=ggterm0*sig0*JAC0*gg0;\n\n\n",
  StyleBox["(* total *)",
    FontColor->RGBColor[1, 0, 0]],
  "\nsig=0;\nsig=sig+qqterm;\nsig=sig+qgterm;\nsig=sig+ggterm+ggterm0;\n\
sig=sig*389379660; (*to picobarns*)\n\nReturn[sig];\n\n];\n"
}], "Input"],

Cell[CellGroupData[{

Cell["\<\
virt=NIntegrate[dsigmaBV[xvar,100,14000,100,100],{xvar,0,1}];
virt\
\>", "Input"],

Cell[BoxData[
    \(TraditionalForm\`33.56877602575538`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
eps=0.0000000001;
real=Vegas[dsigmaR[xvar,yvar,100,14000,100,100],{xvar,eps,1-eps},{yvar,eps,1-\
eps},Compiled->False,NStart->1000,MaxPoints->10000]\
\>", "Input"],

Cell[BoxData[
    \(TraditionalForm\`"\nIteration 1:  1000 integrand evaluations so far\n\
[1] 16.6638 +- 0.729445  \tchisq -0 (0 df)"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"\nIteration 2:  2500 integrand evaluations so far\n\
[1] 16.6521 +- 0.173781  \tchisq 0.000273976 (1 df)"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`$Aborted\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["asNLO[100,5]", "Input"],

Cell[BoxData[
    \(TraditionalForm\`0.11636176382460801`\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
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WindowSize->{872, 573},
WindowMargins->{{131, Automatic}, {106, Automatic}}
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*)



(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)