main51
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// main51.cc is a part of the PYTHIA event generator.
// Copyright (C) 2024 Torbjorn Sjostrand.
// PYTHIA is licenced under the GNU GPL v2 or later, see COPYING for details.
// Please respect the MCnet Guidelines, see GUIDELINES for details.
// Keywords:
// Parton distribution
// LHAPDF
// Test of LHAPDF interface and whether PDF's behave sensibly.
// October 2017: updated to test external LHAPDF6 vs internal LHAGrid1.
#include "Pythia8/Pythia.h"
#include "Pythia8/Plugins.h"
using namespace Pythia8;
//==========================================================================
// Integration to check momentum sum rule.
double integrate(PDFPtr nowPDF, double Q2) {
// Number of points, x ranges and initial values.
int nLin = 980;
int nLog = 1000;
double xLin = 0.02;
double xLog = 1e-8;
double dxLin = (1. - xLin) / nLin;
double dxLog = log(xLin / xLog) / nLog;
double sum = 0.;
double x, sumNow;
// Integration at large x in linear steps.
for (int iLin = 0; iLin < nLin; ++iLin) {
x = xLin + (iLin + 0.5) * dxLin;
sumNow = nowPDF->xf( 21, x, Q2) + nowPDF->xf( 22, x, Q2);
for (int i = 1; i < 6; ++i)
sumNow += nowPDF->xf( i, x, Q2) + nowPDF->xf( -i, x, Q2);
sum += dxLin * sumNow;
}
// Integration at small x in logarithmic steps.
for (int iLog = 0; iLog < nLog; ++iLog) {
x = xLog * pow( xLin / xLog, (iLog + 0.5) / nLog );
sumNow = nowPDF->xf( 21, x, Q2) + nowPDF->xf( 22, x, Q2);
for (int i = 1; i < 6; ++i)
sumNow += nowPDF->xf( i, x, Q2) + nowPDF->xf( -i, x, Q2);
sum += dxLog * x * sumNow;
}
// Done.
return sum;
}
//==========================================================================
int main() {
// Info member for possible error printouts etc.
Logger logger;
// Pointers to external LHAPDF6 and internal LHAGrid1 PDF packages,
// for the same NNPDF3.1 QCD+QED NNLOPDF set, the central member.
PDFPtr extPDF = make_plugin<PDF>("libpythia8lhapdf6.so", "LHAPDF6");
extPDF->init(2212, "NNPDF31_nnlo_as_0118_luxqed", 0, &logger);
if (!extPDF) return 1;
PDFPtr intPDF = make_shared<LHAGrid1>
( 2212, "20", "../share/Pythia8/pdfdata/", &logger);
// Alternative: compare two Pomeron PDF's. Boost second by factor 2.
//PDF* extPDF = new PomFix( 990, -0.2, 2.5, 0., 3., 0.4, 0.5);
//PDF* intPDF = new PomH1Jets( 990, 2.);
//PDF* extPDF = new PomH1FitAB( 990, 2);
//PDF* intPDF = new PomH1FitAB( 990, 3);
// Allow extrapolation of PDF's beyond x and Q2 boundaries, at own risk.
// Default behaviour is to freeze PDF's at boundaries.
intPDF->setExtrapolate(true);
extPDF->setExtrapolate(true);
// Histogram F(x, Q2) = (9/4) x*g(x, Q2) + sum_{i = q, qbar} x*f_i(x, Q2)
// for range 10^{-8} < x < 1 logarithmic in x and for Q2 = 4 and 100.
Hist extF4("F( x, Q2 = 4) external", 80 , 1e-8, 1., true);
Hist intF4("F( x, Q2 = 4) internal", 80 , 1e-8, 1., true);
Hist ratF4("F( x, Q2 = 4) internal/external", 80 , 1e-8, 1., true);
Hist extF100("F( x, Q2 = 100) external", 80 , 1e-8, 1., true);
Hist intF100("F( x, Q2 = 100) internal", 80 , 1e-8, 1., true);
Hist ratF100("F( x, Q2 = 100) internal/external", 80 , 1e-8, 1., true);
// Loop over the two Q2 values.
for (int iQ = 0; iQ < 2; ++iQ) {
double Q2 = (iQ == 0) ? 4. : 100;
// Loop over x values, in a logarithmic scale.
for (int iX = 0; iX < 80; ++iX) {
double xLog = -(0.1 * iX + 0.05);
double x = pow( 10., xLog);
// Evaluate external summed PDF, with colour factor 9/4 for gluons.
double extSum = 2.25 * extPDF->xf( 21, x, Q2);
for (int i = 1; i < 6; ++i)
extSum += extPDF->xf( i, x, Q2) + extPDF->xf( -i, x, Q2);
if (iQ == 0) extF4.fill ( x, extSum );
else extF100.fill ( x, extSum );
// Evaluate internal summed PDF, with colour factor 9/4 for gluons.
double intSum = 2.25 * intPDF->xf( 21, x, Q2);
for (int i = 1; i < 6; ++i)
intSum += intPDF->xf( i, x, Q2) + intPDF->xf( -i, x, Q2);
if (iQ == 0) intF4.fill ( x, intSum );
else intF100.fill ( x, intSum );
// End loops over x and Q2 values.
}
}
// Show F(x, Q2) and their ratio internal/external.
ratF4 = intF4 / extF4;
ratF100 = intF100 / extF100;
cout << extF4 << intF4 << ratF4 << extF100 << intF100 << ratF100;
// Histogram momentum sum as a function of Q2.
Hist extXSum("momentum sum(Q2) - 1 external", 100, 1e-2, 1e8, true);
Hist intXSum("momentum sum(Q2) - 1 internal", 100, 1e-2, 1e8, true);
Hist difXSum("momentum sum(Q2) internal - external", 100, 1e-2, 1e8, true);
// Loop over Q2 values.
for (int iQ = 0; iQ < 100; ++iQ) {
double log10Q2 = -2.0 + 0.1 * iQ + 0.05;
double Q2 = pow( 10., log10Q2);
// Evaluate external and internal momentum sums.
double extSum = integrate( extPDF, Q2);
extXSum.fill( Q2, extSum - 1.);
double intSum = integrate( intPDF, Q2);
intXSum.fill( Q2, intSum - 1.);
}
// Show momentum sum as a function of Q2.
difXSum = intXSum - extXSum;
cout << extXSum << intXSum << difXSum;
// Write Python code that can generate a PDF file with the distributions.
// Note: curve and histogram style deliberately mixed for clarity.
HistPlot hpl("main51plot");
hpl.frame( "out51plot", "Summed PDF distribution at $Q^2 = 4$", "$x$",
"$(9/4)x g(x, Q^2) + \\sum_{q} (xq(x, Q^2) + x\\overline{q}(x, Q^2)$");
hpl.add( extF4, "-", "LHAPDF6");
hpl.add( intF4, "h,red", "internal");
hpl.plot();
hpl.frame( "", "Summed PDF distribution at $Q^2 = 100$", "$x$",
"$(9/4)x g(x, Q^2) + \\sum_{q} (xq(x, Q^2) + x\\overline{q}(x, Q^2)$");
hpl.add( extF100, "-", "LHAPDF6");
hpl.add( intF100, "h,red", "internal");
hpl.plot();
hpl.frame( "", "Momentum sum as a function of $Q^2$", "$Q^2$",
"$( \\int_0^1 \\sum_{q,\\overline{q},g, \\gamma} xf_i(x, Q^2)"
"\\, \\mathrm{d}x ) - 1$");
hpl.add( extXSum, "-", "LHAPDF6");
hpl.add( intXSum, "h,red", "internal");
hpl.plot();
// Done.
return 0;
}