Frascati: phenHiggs.nb

File phenHiggs.nb, 84.8 KB (added by anonymous, 7 years ago)
Line 
1(************** Content-type: application/mathematica **************
2
3                    Mathematica-Compatible Notebook
4
5This notebook can be used with any Mathematica-compatible
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36*******************************************************************)
37
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46(*WindowFrame->Normal*)
47
48
49
50Notebook[{
51
52Cell[CellGroupData[{
53Cell["Phenomenology of pp\[Rule]H+X at NLO", "Subtitle"],
54
55Cell[CellGroupData[{
56
57Cell["Introduction", "Section"],
58
59Cell[TextData[{
60  StyleBox["In this notebook we calculate the inclusive cross section for \
61Higgs production at hadron colliders, at NLO in the strong coupling. We use \
62the analytic results obtained in a previous notebook corresponding to the \
63original calculation by Sally Dawson (Nuclear Physics B (1991) 283). To get \
64useful numbers we use a modern set of PDF, i.e. the MRST as implemented in ",
65    FontSize->16],
66  StyleBox["Mathematica",
67    FontSize->16,
68    FontSlant->"Italic"],
69  StyleBox[" by J.Andersen (many thanks!).  A description of the calculation, \
70including the formulas used here for the numerical results, is given in the \
71notes.",
72    FontSize->16]
73}], "Text"]
74}, Closed]],
75
76Cell[CellGroupData[{
77
78Cell["Preliminaries", "Section"],
79
80Cell["\<\
81Off[General::spell];
82Off[General::spell1];
83Clear[\"Global`*\"];\
84\>", "Input"],
85
86Cell[CellGroupData[{
87
88Cell["Install Vegas", "Subsection"],
89
90Cell["\<\
91I use the  Vegas package of CUBA library of T. Hahn \
92(hep-ph/0404043). If you do not want to use it, use NIntegrate instead of \
93Vegas\
94\>", "Text"],
95
96Cell[CellGroupData[{
97
98Cell[BoxData[
99    \(Install["\</Users/fabiomaltoni/Physics/Codes/CUBA/VegasX\>"]
100      Install["\</Users/fabiomaltoni/Physics/Codes/CUBA/SuaveX\>"]\)], "Input"],
101
102Cell[BoxData[
103    \(TraditionalForm\`LinkObject[
104        "/Users/fabiomaltoni/Physics/Codes/CUBA/SuaveX", 3, 3]\ LinkObject[
105        "/Users/fabiomaltoni/Physics/Codes/CUBA/VegasX", 2, 2]\)], "Output"]
106}, Open  ]]
107}, Closed]],
108
109Cell[CellGroupData[{
110
111Cell["Call special graphics routines", "Subsection"],
112
113Cell["\<\
114<< Graphics`Colors`;
115<< Graphics`Graphics`;\
116\>", "Input"]
117}, Closed]],
118
119Cell[CellGroupData[{
120
121Cell["Install PDF'S: for help read the PDF-HOWTO document", "Subsection"],
122
123Cell[CellGroupData[{
124
125Cell[BoxData[{
126    \(SetDirectory["\<~/Physics/Teaching/pp>Higgs\ at\ NLO/Jeppe\>"]\), "\
127\[IndentingNewLine]",
128    \(Install["\<pdf.exe\>"]\)}], "Input"],
129
130Cell[BoxData[
131    \(TraditionalForm\`"/Users/fabiomaltoni/Physics/Teaching/pp>Higgs at \
132NLO/Jeppe"\)], "Output"],
133
134Cell[BoxData[
135    \(TraditionalForm\`LinkObject["./pdf.exe", 4, 4]\)], "Output"]
136}, Open  ]],
137
138Cell[CellGroupData[{
139
140Cell["\<\
141
142<<\"loadCTEQ5.m\";\
143\>", "Input"],
144
145Cell[BoxData[
146    \(TraditionalForm\`"Loading Package: PDF"\)], "Print"],
147
148Cell[BoxData[
149    \(TraditionalForm\`"PDF's from CTEQ5"\)], "Print"],
150
151Cell[BoxData[
152    \(TraditionalForm\`"Eur.Phys.J.C12:375-392,2000 "\)], "Print"],
153
154Cell[BoxData[
155    \(TraditionalForm\`"*** Warning *** Unofficial release. "\)], "Print"],
156
157Cell[BoxData[
158    \(TraditionalForm\`"*** Cross-check with official Fortran code."\)], \
159"Print"],
160
161Cell[BoxData[
162    \(TraditionalForm\`" Version 1.0: Written by Tamara Trout & Fred Olness, \
163October 1, 2000"\)], "Print"],
164
165Cell[BoxData[
166    \(TraditionalForm\`" "\)], "Print"],
167
168Cell[BoxData[
169    \(TraditionalForm\`"In case of problems, contact:"\)], "Print"],
170
171Cell[BoxData[
172    \(TraditionalForm\`"Fred Olness: olness@mail.physics.smu.edu"\)], "Print"]
173}, Open  ]],
174
175Cell[CellGroupData[{
176
177Cell["\<\
178Wrapper to call the pdf. Notation is self-explanatory. Just notice \
179that all parton distribution codes usually return x f(x). To avoid confusion, \
180at expense of a couple more floating point operations, I divide all the \
181values by the corresponding x.  pdfcall calculates the parton-parton \
182luminoties, gg qg, qq~\
183\>", "Subsubsection"],
184
185Cell["\<\
186(* MRST *)
187
188pdfMRST[X1_,X2_,q_]:=Module[
189{Q,xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF,pd1,pd2,xgg,xqg,xqq},
190Q=q*1.;
191xgDF =f[3,X1,Q]/X1;
192xdbDF=f[8,X1,Q]/X1;
193xdDF =f[2,X1,Q]/X1+xdbDF;
194xubDF=f[4,X1,Q]/X1;
195xuDF =f[1,X1,Q]/X1+xubDF;
196xsDF =f[6,X1,Q]/X1;
197xcDF =f[5,X1,Q]/X1;
198xbDF =f[7,X1,Q]/X1;
199
200pd1={xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF};
201xgDF =f[3,X2,Q]/X2;
202xdbDF=f[8,X2,Q]/X2;
203xdDF =f[2,X2,Q]/X2+xdbDF;
204xubDF=f[4,X2,Q]/X2;
205xuDF =f[1,X2,Q]/X2+xubDF;
206xsDF =f[6,X2,Q]/X2;
207xcDF =f[5,X2,Q]/X2;
208xbDF =f[7,X2,Q]/X2;
209pd2={xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF};
210
211
212xgg=pd1[[1]]*pd2[[1]];
213xqg=pd1[[1]]*(pd2[[2]]+pd2[[3]]+pd2[[4]]+pd2[[5]]+2(pd2[[6]]+pd2[[7]]+pd2[[8]]\
214))+
215   pd2[[1]]*(pd1[[2]]+pd1[[3]]+pd1[[4]]+pd1[[5]]+2(pd1[[6]]+pd1[[7]]+pd1[[8]])\
216);
217xqq=pd1[[2]]*pd2[[3]]+pd1[[4]]*pd2[[5]]+pd1[[3]]*pd2[[2]]+pd1[[5]]*pd2[[4]]+
218   2(pd1[[6]] pd2[[6]]+pd1[[7]] pd2[[7]]+pd1[[8]] pd2[[8]]);
219 
220  Return[{xgg,xqg,xqq}];
221];\
222\>", "Input"],
223
224Cell["\<\
225
226(* cteq5 *)\
227\>", "Input"],
228
229Cell["\<\
230pdfCTEQ[X1_,X2_,q_]:=Module[
231{Q,pd1,pd2,xgg,xqg,xqq},
232Q=q*1.;
233
234pd1={cteq5pdf[1,0,X1,Q],
235     cteq5pdf[1,2,X1,Q],
236     cteq5pdf[1,-2,X1,Q],
237     cteq5pdf[1,1,X1,Q],
238     cteq5pdf[1,-1,X1,Q],
239     cteq5pdf[1,3,X1,Q],
240     cteq5pdf[1,4,X1,Q],
241     cteq5pdf[1,5,X1,Q]};
242pd2={cteq5pdf[1,0,X2,Q],
243     cteq5pdf[1,2,X2,Q],
244     cteq5pdf[1,-2,X2,Q],
245     cteq5pdf[1,1,X2,Q],
246     cteq5pdf[1,-1,X2,Q],
247     cteq5pdf[1,3,X2,Q],
248     cteq5pdf[1,4,X2,Q],
249     cteq5pdf[1,5,X2,Q]};
250     
251xgg=pd1[[1]]*pd2[[1]];
252xqg=pd1[[1]]*(pd2[[2]]+pd2[[3]]+pd2[[4]]+pd2[[5]]+2(pd2[[6]]+pd2[[7]]+pd2[[8]]\
253))+
254   pd2[[1]]*(pd1[[2]]+pd1[[3]]+pd1[[4]]+pd1[[5]]+2(pd1[[6]]+pd1[[7]]+pd1[[8]])\
255);
256xqq=pd1[[2]]*pd2[[3]]+pd1[[4]]*pd2[[5]]+pd1[[3]]*pd2[[2]]+pd1[[5]]*pd2[[4]]+
257   2(pd1[[6]] pd2[[6]]+pd1[[7]] pd2[[7]]+pd1[[8]] pd2[[8]]);
258 
259  Return[{xgg,xqg,xqq}];
260];
261
262pdfCTEQLO[X1_,X2_,q_]:=Module[
263{Q,xgDF,xdDF,xdbDF,xuDF,xubDF,xsDF,xcDF,xbDF,pd1,pd2,xgg,xqg,xqq},
264Q=q*1.;
265
266pd1={cteq5pdf[3,0,X1,Q],
267     cteq5pdf[3,2,X1,Q],
268     cteq5pdf[3,-2,X1,Q],
269     cteq5pdf[3,1,X1,Q],
270     cteq5pdf[3,-1,X1,Q],
271     cteq5pdf[3,3,X1,Q],
272     cteq5pdf[3,4,X1,Q],
273     cteq5pdf[3,5,X1,Q]};
274pd2={cteq5pdf[3,0,X2,Q],
275     cteq5pdf[3,2,X2,Q],
276     cteq5pdf[3,-2,X2,Q],
277     cteq5pdf[3,1,X2,Q],
278     cteq5pdf[3,-1,X2,Q],
279     cteq5pdf[3,3,X2,Q],
280     cteq5pdf[3,4,X2,Q],
281     cteq5pdf[3,5,X2,Q]};
282     
283xgg=pd1[[1]]*pd2[[1]];
284xqg=pd1[[1]]*(pd2[[2]]+pd2[[3]]+pd2[[4]]+pd2[[5]]+2(pd2[[6]]+pd2[[7]]+pd2[[8]]\
285))+
286   pd2[[1]]*(pd1[[2]]+pd1[[3]]+pd1[[4]]+pd1[[5]]+2(pd1[[6]]+pd1[[7]]+pd1[[8]])\
287);
288xqq=pd1[[2]]*pd2[[3]]+pd1[[4]]*pd2[[5]]+pd1[[3]]*pd2[[2]]+pd1[[5]]*pd2[[4]]+
289   2(pd1[[6]] pd2[[6]]+pd1[[7]] pd2[[7]]+pd1[[8]] pd2[[8]]);
290 
291  Return[{xgg,xqg,xqq}];
292];\
293\>", "Input"]
294}, Open  ]],
295
296Cell[CellGroupData[{
297
298Cell["Decide the pdf family to be used ", "Subsubsection"],
299
300Cell["pdfcall[x__] = pdfCTEQ[x];", "Input"]
301}, Open  ]]
302}, Open  ]],
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304Cell[CellGroupData[{
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306Cell["\<\
307Alpha_S: Very basic implementation of Alpha_S.
308Check that the value of Lamda_4 or Lambda_5 is consistent with that of the \
309PDF.
310One simple, but indirect way to do it is to compare the value of alphas(MZ) \
311with the one quoted by MRST.\
312\>", "Subsection"],
313
314Cell[BoxData[{
315    \(\(b[nf_] := \(\((33 - 2\ nf)\)/12\)/
316          Pi;\)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
317\ \ \ \), "\[IndentingNewLine]",
318    \(\(bp[
319          nf_] := \(\(\((153 - 19\ nf)\)/2\)/
320            Pi\)/\((33 - 2\ nf)\);\)\), "\[IndentingNewLine]",
321    \(\(t[nf] :=
322        Log[q^2/\[CapitalLambda][nf]^2];\)\), "\[IndentingNewLine]",
323    \(\(\(mb = 4.75;\)\(\[IndentingNewLine]\)
324    \)\), "\[IndentingNewLine]",
325    \(\(\[CapitalLambda][5] = 0.146;\)\), "\[IndentingNewLine]",
326    \(\(asLO[q_, nf_] = 1/\((b[nf]\ t[nf])\);\)\), "\n",
327    \(\(\[CapitalLambda][5] = 0.226;\)\), "\[IndentingNewLine]",
328    \(\(asNLO[q_, nf_] =
329        1/\((b[nf]\ t[nf])\) \((1 -
330              bp[nf]/b[nf]\ Log[t[nf]]/t[nf])\);\)\)}], "Input"],
331
332Cell[CellGroupData[{
333
334Cell["\<\
335Check the values of alpha_S at the scale MZ\
336\>", "Subsubsection"],
337
338Cell[CellGroupData[{
339
340Cell["asNLO[91.118,5]", "Input"],
341
342Cell[BoxData[
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345}, Open  ]]
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348Cell[CellGroupData[{
349
350Cell["Color factors ", "Subsection"],
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352Cell["\<\
353CF=4/3;
354CA=3;
355nf=5;
356TF=1/2;
357b0=11/6 CA -2 nf TF/3;
358\
359\>", "Input"]
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361}, Open  ]],
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363Cell[CellGroupData[{
364
365Cell["LO cross section", "Section"],
366
367Cell[CellGroupData[{
368
369Cell["\<\
370Integral of the LO loop. The sign of the Imaginary part is given by \
371the usual prescription mt^2-i eps which is equivalent to t+i eps in the \
372notation below.
373t=mh^2/4/mt^2;\
374\>", "Subsubsection"],
375
376Cell[" ", "Input"],
377
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379
380Cell["\<\
381eps=0.00000001;
382inte[t_]=3*Integrate[(1-4 x y)/(1-4 t x y),{x,0,1},{y,0,1-x}]//Simplify;
383Plot[{Re[inte[t+I eps]],Im[inte[t+I \
384eps]]},{t,0,10},PlotStyle\[Rule]{{Blue,Thickness[0.007]},{Red,Thickness[0.007]\
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386\>", "Input"],
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1073\>"],
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1076}, Open  ]],
1077
1078Cell["\<\
1079Plot of the real and imaginary part of 3*I(a) as defined in the \
1080notes (I use 3*I(a) so that the function goes to 1 as a->0.)\
1081\>", "Text"]
1082}, Open  ]],
1083
1084Cell[CellGroupData[{
1085
1086Cell[TextData[{
1087  "Function to be integrated to get the LO cross section. In general, we use \
1088the convention that all functions to be numerically integrated in the \
1089hypercubes ",
1090  Cell[BoxData[
1091      \(TraditionalForm\`\([0, 1]\)\^d\)]],
1092  ", where d is the dimension of the integration space. dsigma depends on the \
1093Higgs mass (mh), the total collider energy (sqrtS) and from the arbitrary \
1094normalization and factorization scales (mur,muf)."
1095}], "Subsubsection"],
1096
1097Cell["\<\
1098dsigmaLO[zz_,mh_,sqrtS_,muf_,mur_]:=Module[
1099{y,x1,x2,gg0,qg0,qq0,s0,ymin,ymax,JAC,v,S,tau0},
1100Muf=muf*1.;
1101v=246.;
1102S=sqrtS^2;
1103tau0=mh^2/S;
1104ymax=-Log[Sqrt[tau0]];
1105ymin=-ymax;
1106y=ymin+(ymax-ymin)*zz;
1107JAC=ymax-ymin;
1108x1=Sqrt[tau0] Exp[y];
1109x2=Sqrt[tau0] Exp[-y];
1110{gg0,qg0,qq0}=pdfCTEQLO[x1,x2,Muf];
1111s0=asLO[mur,5]^2/576/Pi/v^2*tau0;
1112s0=s0*gg0;
1113s0=s0*389379660; (*to picobarns*)
1114s0=s0*JAC;
1115Return[s0];
1116];\
1117\>", "Input"],
1118
1119Cell[CellGroupData[{
1120
1121Cell["sLO=NIntegrate[dsigmaLO[xx,100,14000,100,100],{xx,0,1}]", "Input"],
1122
1123Cell[BoxData[
1124    \(TraditionalForm\`28.056643821030747`\)], "Output"]
1125}, Open  ]]
1126}, Open  ]],
1127
1128Cell[CellGroupData[{
1129
1130Cell["\<\
1131Get the cross section for various Higgs masses and including the \
1132form factor of the loop.
1133I first build a table with the results of the cross section in picobarns, and \
1134then plot it.\
1135\>", "Subsection"],
1136
1137Cell["\<\
1138resEFT=Table[{i,NIntegrate[dsigmaLO[x,i*1.,14000.,i*1.,i*1.],{x,0,1}\
1139]},{i,20,600,10}];\
1140\>", "Input"],
1141
1142Cell["\<\
1143resFULL=Table[{resEFT[[i]][[1]],Abs[inte[resEFT[[i]][[1]]^2/175^2/4]\
1144]^2*resEFT[[i]][[2]]},{i,1,Length[resEFT]}];\
1145\>", "Input"],
1146
1147Cell["resFULL", "Input"],
1148
1149Cell[CellGroupData[{
1150
1151Cell[TextData[{
1152  "Show[LogListPlot[resEFT, ",
1153  StyleBox["PlotJoined", "MR"],
1154  " ",
1155  StyleBox["->", "MR"],
1156  " ",
1157  StyleBox["True,", "MR"],
1158  "PlotStyle\[Rule]{Red}],\nplotFULL=LogListPlot[resFULL, ",
1159  StyleBox["PlotJoined", "MR"],
1160  " ",
1161  StyleBox["->True,", "MR"],
1162  "PlotStyle\[Rule]{Blue}]];\n\n"
1163}], "Input"],
1164
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2055\>"],
2056  ImageRangeCache->{{{0, 412}, {254.125, 0}} -> {-58.8613, -0.530814, \
20571.63559, 0.0117063}}]
2058}, Open  ]],
2059
2060Cell["\<\
2061Cross section (pb) as a function of the Higgs mass. This plot shows \
2062how well the EFT does. For a Higgs<200 GeV the approximation is very \
2063good.\
2064\>", "Text"]
2065}, Open  ]],
2066
2067Cell[CellGroupData[{
2068
2069Cell["Various ways to do the integration over the x1 and x2.", "Subsection"],
2070
2071Cell[CellGroupData[{
2072
2073Cell["\<\
2074
2075uno=Integrate[x1*x2,{x1,t0,1},{x2,t0/x1,1}]//Expand
2076due=Integrate[ta,{ta,t0,1},{y,Log[Sqrt[ta]],-Log[Sqrt[ta]]}]//PowerExpand//\
2077Expand
2078tre=Integrate[t0/z \
2079t0/z^2,{z,t0,1},{y,Log[Sqrt[t0/z]],-Log[Sqrt[t0/z]]}]//PowerExpand//Expand\
2080\>\
2081", "Input"],
2082
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2084    \(TraditionalForm\`1\/2\ \(log(t0)\)\ t0\^2 - t0\^2\/4 + 1\/4\)], "Output"],
2085
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2097Cell["NLO cross section", "Section"],
2098
2099Cell["\<\
2100We have integrate over the angular variables, so we are only left \
2101with two integrations. One is over z (=mh/S/x1/x2) and the other over the \
2102rapidity y of the partonic cms. For every point in the phase space we have to \
2103calculate an event and a corresponding counter-event with z=1 to implement \
2104the + distributions in the gg channel. Various contributions add to the final \
2105result:
2106
2107virtual: gg>h  at 1-loop + corrections to the effective lagrangian (UV and IR \
2108divergent)
2109real: qq~ >h g (finite)
2110           qg > qh (collinear divergent)
2111            gg>gh  (soft and collinear divergent)
2112\
2113\>", "Text",
2114  FontSize->16],
2115
2116Cell[CellGroupData[{
2117
2118Cell["Born+Virtual ", "Subsection"],
2119
2120Cell[TextData[{
2121  "dsigmaBV[yy_,mh_,sqrtS_,muf_,mur_]:=Module[\n",
2122  StyleBox["(* local variables *)",
2123    FontColor->RGBColor[0, 1, 0]],
2124  "\n{y0,x10,x20,sig0,ymax0,JAC0,v,S,tau0,beta,gg0,qg0,qq0},\nMuf=muf 1.;\n\
2125Mur=mur 1.;\nv=246.;\nS=sqrtS^2;\ntau0=mh^2/S;\nbeta=Sqrt[1-tau0];\n\n",
2126  StyleBox["(* calculate quantities for z=1 *)",
2127    FontColor->RGBColor[1, 0, 0]],
2128  "\nymax0=-Log[Sqrt[tau0]];\ny0=-ymax0+2*ymax0*yy;\nJAC0=2*ymax0;\n\
2129x10=Sqrt[tau0] Exp[y0];\nx20=Sqrt[tau0] Exp[-y0];\n\
2130{gg0,qg0,qq0}=pdfcall[x10,x20,Muf];\n\n",
2131  StyleBox["(* sigma0 *)",
2132    FontColor->RGBColor[1, 0, 0]],
2133  "\nsig0=asNLO[Mur,5]^2/576/Pi/v^2*tau0;\nsig0=sig0+sig0*asNLO[Mur,5]/2/Pi*\n\
2134(11/3 CA+ 2 Pi^2 - 2 b0 2 Log[Muf/Mur]+\n16 CA Log[beta] Log[mh/Muf]+16 CA \
2135Log[beta]^2);\nsig0=sig0*gg0;\nsig0=sig0*389379660; (*to picobarns*)\n\
2136sig0=sig0*JAC0;\n\n\
2137(*Print[{muf,mur,v,S,tau0,beta,ymax0,y0,JAC0,x10,x20,gg0,qg0,qq0,sig0}];*)\n\
2138Return[sig0];\n];"
2139}], "Input"]
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2143
2144Cell["Real contributions", "Subsection"],
2145
2146Cell[TextData[{
2147  "dsigmaR[xx_,yy_,mh_,sqrtS_,muf_,mur_]:=Module[\n",
2148  StyleBox["(* local variables *)",
2149    FontColor->RGBColor[0, 1, 0]],
2150  "\n{v,S,tau0,\n y,y0,z,tau,\n x1,x2,x10,x20,\n ymax0,ymax,\n JAC,JAC0,\n \
2151gg,qg,qq,gg0,qg0,qq0,\n qqterm,qgterm,ggterm,ggterm0,\n sig,sig0,\n Muf},\n\n\
2152v=246.;\nS=sqrtS^2;\ntau0=mh^2/S;\nMuf=muf*1.0;\n\n",
2153  StyleBox["(* calculate quantities for an event *)",
2154    FontColor->RGBColor[1, 0, 0]],
2155  "\nz=tau0+(1-tau0)*xx;\ntau=tau0/z;\nymax =-Log[Sqrt[tau]];\n\
2156y=-ymax+2*ymax*yy;\nJAC =2*ymax*(1-tau0)*tau0/z^2;\nx1=Sqrt[tau] Exp[y];\n\
2157x2=tau/x1;\n",
2158  StyleBox["(* call the pdf *)\n",
2159    FontColor->RGBColor[1, 0, 0]],
2160  "\n{gg,qg,qq}=pdfcall[x1,x2,Muf];\n\n",
2161  StyleBox["(* calculate quantities for counter-event *)",
2162    FontColor->RGBColor[1, 0, 0]],
2163  "\nymax0=-Log[Sqrt[tau0]];\ny0=-ymax0+2*ymax0*yy;\n\
2164JAC0=2*ymax0*(1-tau0)*tau0;\nx10=Sqrt[tau0] Exp[y0];\nx20=tau0/x10;\n",
2165  StyleBox["(* call the pdf at z=1 *)",
2166    FontColor->RGBColor[1, 0, 0]],
2167  "\n{gg0,qg0,qq0}=pdfcall[x10,x20,Muf];\n\n",
2168  StyleBox["(* sigma0 *)",
2169    FontColor->RGBColor[1, 0, 0]],
2170  "\nsig0=asNLO[mur,5]^2/576/Pi/v^2;\nsig0=sig0*asNLO[mur,5]/2/Pi;\n\n",
2171  StyleBox["(* qq channnel : no counter event *)",
2172    FontColor->RGBColor[1, 0, 0]],
2173  "\nqqterm=64/27*(1-z)^3;\nqqterm=qqterm*sig0*JAC*qq;\n\n",
2174  StyleBox["(* qg channnel : no counter event *)",
2175    FontColor->RGBColor[1, 0, 0]],
2176  "\nqgterm=CF*( (1+(1-z)^2)/z (2*Log[mh/muf]+2 Log[1-z]-Log[z])\n           \
2177+(z^2-3/2(1-z)^2)/z )*z;\nqgterm=qgterm*sig0*JAC*qg;\n\n",
2178  StyleBox["(* gg channnel *)",
2179    FontColor->RGBColor[1, 0, 0]],
2180  "\nggterm=CA*(2 (2 (z/(1-z)+(1-z)/z+z (1-z) )) * (2*Log[mh/muf])-\n       \
218111/3 (1-z)^3/z -\n       4 (1-z+z^2)^2/z/(1-z) Log[z]+\n       8 \
2182(1-z+z^2)^2/z Log[1-z]/(1-z) )*z;\nggterm=ggterm*sig0*JAC*gg;\n",
2183  StyleBox["(* gg counter-event *)",
2184    FontColor->RGBColor[1, 0, 0]],
2185  "\nggterm0=CA*(-4/(1-z) 2*Log[mh/muf] - 8*Log[1-z]/(1-z) );\n\
2186ggterm0=ggterm0*sig0*JAC0*gg0;\n\n\n",
2187  StyleBox["(* total *)",
2188    FontColor->RGBColor[1, 0, 0]],
2189  "\nsig=0;\nsig=sig+qqterm;\nsig=sig+qgterm;\nsig=sig+ggterm+ggterm0;\n\
2190sig=sig*389379660; (*to picobarns*)\n\nReturn[sig];\n\n];\n"
2191}], "Input"],
2192
2193Cell[CellGroupData[{
2194
2195Cell["\<\
2196virt=NIntegrate[dsigmaBV[xvar,100,14000,100,100],{xvar,0,1}];
2197virt\
2198\>", "Input"],
2199
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2207eps=0.0000000001;
2208real=Vegas[dsigmaR[xvar,yvar,100,14000,100,100],{xvar,eps,1-eps},{yvar,eps,1-\
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2210\>", "Input"],
2211
2212Cell[BoxData[
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2214[1] 16.6638 +- 0.729445  \tchisq -0 (0 df)"\)], "Print"],
2215
2216Cell[BoxData[
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2218[1] 16.6521 +- 0.173781  \tchisq 0.000273976 (1 df)"\)], "Print"],
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