## main484

Back to index.

    // main484.cc is a part of the PYTHIA event generator.
    // Copyright (C) 2026 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.

    // Authors:
    //            Marius Utheim
    //            Torbjorn Sjostrand

    // Keywords:
    //            Cosmic ray cascade
    //            Switch beam
    //            Switch collision energy

    // This example demonstrates the production of atmospheric showers.
    // It is based on the model and studies in Eur. Phys. J. C82 (2022) 21
    // (arXiv:2108.03481 [hep-ph]), notably for hadron-nitrogen collisions.
    // Reminder: for vertex Vec4 the components are labelled (px, py, pz, e),
    // but actually represent (x, y, z, t) values.

    #include "Pythia8/Pythia.h"
    #include "Pythia8Plugins/PythiaCascade.h"

    using namespace Pythia8;

    //==========================================================================

    // Note: when a hadron interacts with a medium particle, the latter is added
    // to the event record. This program uses these additional status codes for
    // target particles in the medium:
    //  181: the first (or only) target nucleon in a collision.
    //  182: nucleons from further subcollisions with the same target nucleus.

    // Conversion factor between mm and km.
    constexpr double KM2MM = 1.e6;

    // Conversion factor for kg/m^3 to GeV/(c^2 mm mb)
    constexpr double kg_m3_to_GeV_c2mm1mb1
      =  5.60958865e26 // kg to GeV/c2
        * 0.001         // m^-1 to mm^-1
        * 1e-31;        // m^-2 to mb^-1

    // Medium parameters
    constexpr double mAir = 0.9315;
    constexpr double mediumDensity = 1.225 * kg_m3_to_GeV_c2mm1mb1 / mAir;
    constexpr double rhoAir = 1.225e-4; // g cm^-2 mm^-1
    constexpr double mediumHeight = 100 * KM2MM;
    constexpr double H = 10.4 * KM2MM;

    //==========================================================================

    // Configuration of the atmospheric model.

    struct Configuration {
      // Description of the configuration, to be used when plotting.
      string legend;
      // Whether the atmosphere should be exponentially attenuated, or uniform.
      bool doExponential;
      // Whether the medium particles are clustered into ions or a p/n gas.
      bool doHeavyIon;
      // The zenith angle of the primary particle.
      double zenithAngle;
      // Hadrons below the kinetic energy threshold cannot interact with medium.
      double eKinMin;

      // Get the height above ground of the primary particle when cascade begins.
      double initialHeight() {
        return doExponential ? mediumHeight : H;
      }

      // Get the medium depth of a particle at the specified height.
      double getDepth(double h) {
        return 1. / cos(zenithAngle)
            * ( doExponential ? rhoAir * H * exp(-h / H)
                              : rhoAir * (initialHeight() - h) );
      }
    };

    //==========================================================================

    int main() {

      // Set up four different "atmospheres" to compare.
      constexpr int nCases = 4;
      vector<Configuration> configurations = {
        { "Uniform p/n atmosphere",                false, false, 0.,       0.2 },
        { "Uniform nitrogen",                      false, true,  0.,       0.2 },
        { "Exponential nitrogen",                  true,  true,  0.,       0.2 },
        { "Exponential nitrogen at 45$^{\\circ}$", true,  true,  M_PI / 4, 0.2 },
      };
      vector<string> col = { "r", "b", "k", "g" };

      // Energy of primary incident proton (in GeV).
      double pPri = 1e6;

      // Number of events per case. Only do a few since each shower is so big.
      int nEvent = 100;

      // Set maximum size on the event record, to limit runaway code.
      int maxSize = 2000000;

      // Pythia wrapper for managing the cascade evolution and particle decays.
      PythiaCascade pythiaCascade;
      Rndm& rndm = pythiaCascade.rndm();
      double mp = pythiaCascade.particleData().m0(2212);

      // See the PythiaCascade.h file for documentation, such as init() arguments,
      // notably whether a previous *.mpi file can and should be reused.
      double eKinMin         = 0.3;
      double enhanceSDtarget = 0.5;
      string initFile        = "setups/InitDefaultMPI.cmnd";

      // If any of the underlying Pythia objects failed to initialize,
      // exit with error.
      if (!pythiaCascade.init( eKinMin, enhanceSDtarget, initFile)) return 1;

      // Event record for full cascade evolution.
      Event eventMain;
      eventMain.init( "Full cascade event", &pythiaCascade.particleData());

      // Book histograms.
      double depthMax = 1.5 * rhoAir * H;
      Hist nInt[nCases], diffHad[nCases], diffMuon[nCases], prodnue[nCases],
           prodnumu[nCases];
      for (int iCase = 0; iCase < nCases; ++iCase) {
        nInt[iCase].book("depth of interactions",            100, 0., depthMax);
        diffHad[iCase].book("hadron production-decay depth", 100, 0., depthMax);
        diffMuon[iCase].book("muon production-decay depth",  100, 0., depthMax);
        prodnue[iCase].book("nu_e production depth",         100, 0., depthMax);
        prodnumu[iCase].book("nu_mu production depth",       100, 0., depthMax);
      }

      // Begin loops over cases and events.
      for (int iCase = 0; iCase < nCases; ++iCase)
      for (int iEvent = 0; iEvent < nEvent; ++iEvent) {
        Configuration& config = configurations[iCase];

        // Four-momentum of incoming initiator.
        double pxPri = 0.;
        double pyPri = pPri * sin(config.zenithAngle);
        double pzPri = pPri * cos(config.zenithAngle);
        Vec4 p0(pxPri, pyPri, -pzPri, sqrt(pow2(pPri) + pow2(mp)));

        // Insert primary particle in cleared main event record.
        eventMain.clear();
        eventMain.append(90,  -11, 0, 0, 1, 1, 0, 0, p0, mp);
        eventMain.append(2212, 12, 0, 0, 0, 0, 0, 0, p0, mp);

        // Set initial location of initiator, where z is distance above ground.
        double heightNow = config.initialHeight();
        eventMain[0].yProd(-heightNow * tan(config.zenithAngle));
        eventMain[0].zProd(heightNow);
        eventMain[1].yProd(-heightNow * tan(config.zenithAngle));
        eventMain[1].zProd(heightNow);

        // Loop over particles (usually hadrons) in the main event record.
        for (int iHad = 1; iHad < eventMain.size(); ++iHad) {
          Particle& hadNow = eventMain[iHad];

          // Skip already fragmented/decayed or upwards-moving particles.
          if (!hadNow.isFinal() || hadNow.pz() > 0.) continue;

          // Projectile properties.
          int idNow         = hadNow.id();
          Vec4 pNow         = hadNow.p();
          double mNow       = hadNow.m();
          double eNow       = hadNow.e();
          bool mustDecayNow = false;

          // Find decay vertex for unstable hadrons. (Below ground if no decay.)
          Vec4 vDec = hadNow.canDecay() ? hadNow.vDec() : Vec4( 0., 0., -1., 0.);
          bool canDecayNow = hadNow.canDecay() && vDec.pz() > 0.;

          // Low energy hadrons should not interact with medium.
          // Decay non-hadrons or low-energy ones if decay happens above ground.
          if (!hadNow.isHadron() || eNow - mNow < config.eKinMin) {
            if (canDecayNow) mustDecayNow = true;
            else continue;
          }

          // Get hadron-nucleon cross section for hydrogen or nitrogen atmosphere.
          int  Znow       = (config.doHeavyIon) ?  7 : 1;
          int  Anow       = (config.doHeavyIon) ? 14 : 1;
          double sigmaNow = 0.;
          if (!mustDecayNow) {
            // Set up hadron-nucleon cross sections for the current hadron.
            if (!pythiaCascade.sigmaSetuphN( idNow, pNow, mNow)) {
              if (canDecayNow) mustDecayNow = true;
              else continue;
            }
            else {
              // Get hadron-ion cross section. For media consisting of several
              // different atom types, this should be called once for each type.
              sigmaNow = pythiaCascade.sigmahA(Anow);

              // In this run density is nucleons per volume, not nuclei.
              sigmaNow /= Anow;

              // If the cross section vanishes, decay is the only option.
              if (sigmaNow <= 0.) {
                if (canDecayNow) mustDecayNow = true;
                else continue;
              }
            }
          }

          // Calculate potential interaction vertex, depending on medium.
          Vec4 vInt( 0., 0., -1., 0.);
          Vec4 dirNow = pNow / pNow.pAbs();
          if (!mustDecayNow) {
            // Exponential atmosphere.
            if (config.doExponential) {
              double zNow  = hadNow.zProd();
              double dzds  = hadNow.pz() / hadNow.pAbs();
              double logR  = log(rndm.flat());
              double zNext = -H * log( exp(-zNow / H)
                           + dzds / (H * sigmaNow * mediumDensity) * logR );
              vInt = hadNow.vProd() + (zNext - zNow) * dirNow / dzds;
            // Homogeneous atmosphere.
            } else {
              double freePath = rndm.exp() / (mediumDensity * sigmaNow);
              vInt = hadNow.vProd() + freePath * dirNow;
            }

            // Done if hadron reaches surface before both interaction and decay.
            if (vInt.pz() < 0. && !canDecayNow) continue;

            // Do decay if it happens first.
            if (vDec.pz() > vInt.pz()) mustDecayNow = true;
          }

          // Do decay or collision. Empty event means failure, so skip,
          // which could lead to unintended punch-through of a particle.
          int sizeSave    = eventMain.size();
          Event& eventTmp = (mustDecayNow)
                          ? pythiaCascade.nextDecay(idNow, pNow, mNow, vDec)
                          : pythiaCascade.nextColl( Znow, Anow, vInt);
          if (eventTmp.size() == 0) continue;

          // Update properties of incoming hadron.
          hadNow.statusNeg();
          hadNow.daughters( sizeSave, sizeSave);
          double dTau = ( (mustDecayNow ? vDec.e() : vInt.e())
            - hadNow.tProd() ) * mNow / eNow;
          hadNow.tau( dTau);

          // Append new event to existing and link history.
          eventMain += eventTmp;
          eventMain[sizeSave].mothers( iHad, iHad);

          // Stop generation if event record extremely long.
          if (eventMain.size() > maxSize) {
            cout << " Error: maximum event size exceeded for iCase = "
                 << iCase << " and iEvent = " << iEvent << endl;
            break;
          }

        // End of loop over interactions + decays inside a single cascade.
        }

        // Begin analysis. Loop over all particles to find interaction depths.
        for (Particle& h : eventMain) {
          if (h.status() == -12) continue;
          double depthProd = config.getDepth(h.zProd());
          double depthDec  = config.getDepth(h.isFinal() ? 0. : h.zDec());

          // If particle came from the medium, record the interaction depth.
          if (h.status() == -181 || h.status() == -182) {
            nInt[iCase].fill(depthProd);
          }
          // Otherwise, track depths where particles are created/destroyed.
          else if (h.e() - h.m() > config.eKinMin) {
            if (h.isHadron()) {
              if (h.isFinal())
                diffHad[iCase].fill(depthProd, 1.);
              else {
                diffHad[iCase].fill(min(depthProd, depthDec), 1.);
                diffHad[iCase].fill(max(depthProd, depthDec), -1.);
              }
            }
            else if (h.idAbs() == 13) {
              if (h.isFinal())
                diffMuon[iCase].fill(depthProd, 1.);
              else {
                diffMuon[iCase].fill(min(depthProd, depthDec), 1.);
                diffMuon[iCase].fill(max(depthProd, depthDec), -1.);
              }
            }
            else if (h.idAbs() == 12)
              prodnue[iCase].fill(depthProd, 1.);
            else if (h.idAbs() == 14)
              prodnumu[iCase].fill(depthProd, 1.);
          }
        }

      // End loops over events and cases.
      }

      // Print statistics, mainly for errors.
      pythiaCascade.stat();

      // Book histograms.
      Hist nHad[nCases], nMuon[nCases], nnue[nCases], nnumu[nCases];
      for (int iCase = 0; iCase < nCases; ++iCase) {
        nHad[iCase] .book("", 100, 0., depthMax);
        nMuon[iCase].book("", 100, 0., depthMax);
        nnue[iCase] .book("", 100, 0., depthMax);
        nnumu[iCase].book("", 100, 0., depthMax);

        // Integrate production minus depletion to find particle number by depth.
        double nHadSum = 0., nMuonSum = 0., nnueSum = 0., nnumuSum = 0.;
        for (int i = 1; i <= 100; ++i) {
          double depthNow = depthMax * (i - 0.5) / 100.;
          if (depthNow > configurations[iCase].getDepth(0.)) break;
          nHadSum  += diffHad[iCase] .getBinContent(i);
          nMuonSum += diffMuon[iCase].getBinContent(i);
          nnueSum  += prodnue[iCase] .getBinContent(i);
          nnumuSum += prodnumu[iCase].getBinContent(i);
          nHad[iCase] .fill(depthNow, nHadSum );
          nMuon[iCase].fill(depthNow, nMuonSum);
          nnue[iCase] .fill(depthNow, nnueSum );
          nnumu[iCase].fill(depthNow, nnumuSum);
        }

        // Normalize histograms.
        nInt[iCase].normalizeSpectrum(nEvent);
        nHad[iCase]  /= nEvent;
        nMuon[iCase] /= nEvent;
        nnue[iCase]  /= nEvent;
        nnumu[iCase] /= nEvent;
      }

      // Normalize and plot histograms.
      HistPlot plt("plot484");
      plt.frame("fig484", "Atmospheric depth of p/n interactions",
        "$X$ (g/cm$^2$)", "$(1/n_{ev}) dn_{int}/dX$", 6.4, 4.8);
      for (int iCase = 0; iCase < nCases; ++iCase)
        plt.add(nInt[iCase], "-,"+col[iCase], configurations[iCase].legend);
      plt.plot( 0., depthMax, 0.1, 1e3, true);
      plt.frame("", "Number of hadrons at depth",
        "$X$ (g/cm$^2$)", "$(1/n_{ev}) \\int_0^{X} dn_{had}$", 6.4, 4.8);
      for (int iCase = 0; iCase < nCases; ++iCase)
        plt.add(nHad[iCase], "-,"+col[iCase], configurations[iCase].legend);
      plt.plot( 0., depthMax, 10., 2e4, true);
      plt.frame("", "Number of muons at depth",
        "$X$ (g/cm$^2$)", "$(1/n_{ev}) \\int_0^{X} dn_{\\mu}$", 6.4, 4.8);
      for (int iCase = 0; iCase < nCases; ++iCase)
        plt.add(nMuon[iCase], "-,"+col[iCase], configurations[iCase].legend);
      plt.plot( 0., depthMax, 1., 1e5, true);
      plt.frame("", "Number of e neutrinos at depth",
        "$X$ (g/cm$^2$)", "$(1/n_{ev}) \\int_0^{X} dn_{\\nu_e}$", 6.4, 4.8);
      for (int iCase = 0; iCase < nCases; ++iCase)
        plt.add(nnue[iCase], "-,"+col[iCase], configurations[iCase].legend);
      plt.plot( 0., depthMax, 1., 1e5, true);
      plt.frame("", "Number of mu neutrinos at depth",
        "$X$ (g/cm$^2$)", "$(1/n_{ev}) \\int_0^{X} dn_{\\nu_\\mu}$", 6.4, 4.8);
      for (int iCase = 0; iCase < nCases; ++iCase)
        plt.add(nnumu[iCase], "-,"+col[iCase], configurations[iCase].legend);
      plt.plot( 0., depthMax, 1., 1e5, true);

    }