## main201

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    // main201.cc is a part of the PYTHIA event generator.
    // Copyright (C) 2025 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.
    // Also comparison of 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, summed over flavours..
      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, summed over flavours.
      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.
      // Note: QCD factor 9/4 relevant e.g. for total jet rates.
      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("plot201");
      hpl.frame( "fig201", "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;
    }