## main183

Back to index.

    // main183.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.

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

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

    // This example is based on work from Eur. Phys. J. C82 (2022) 21 and
    // arXiv:2108.03481 [hep-ph]. This example demonstrates the production
    // of atmospheric showers.

    #include "Pythia8/Pythia.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 = 5;

      // Main Pythia object for managing the cascade evolution and
      // particle decays.
      Pythia pythiaMain;
      Event& eventMain = pythiaMain.event;
      Rndm& rndm = pythiaMain.rndm;
      double mp = pythiaMain.particleData.m0(2212);
      // Prepare to do decays but no hard processes.
      pythiaMain.readString("ProcessLevel:all = off");
      pythiaMain.readString("211:mayDecay = on");
      pythiaMain.readString("13:mayDecay  = on");
      pythiaMain.readString("321:mayDecay = on");
      pythiaMain.readString("130:mayDecay = on");
      // Initialize.
      pythiaMain.init();

      // Secondary Pythia object for performing individual collisions.
      Pythia pythiaColl;
      Event& eventColl = pythiaColl.event;
      // Variable incoming beam type and energy.
      pythiaColl.readString("Beams:allowVariableEnergy = on");
      pythiaColl.readString("Beams:allowIDAswitch = on");
      // Set up for fixed-target collisions.
      pythiaColl.readString("Beams:frameType = 3");
      pythiaColl.settings.parm("Beams:pzA", -pPri);
      pythiaColl.readString("Beams:pzB = 0.");
      // Must use the soft and low-energy QCD processes.
      pythiaColl.readString("SoftQCD:all = on");
      pythiaColl.readString("LowEnergyQCD:all = on");
      // Decays to be done by pythiaMain.
      pythiaColl.readString("HadronLevel:Decay = off");
      // Reduce printout and relax energy-momentum conservation.
      pythiaColl.readString("Print:quiet = on");
      pythiaColl.readString("Check:epTolErr = 0.1");
      // Reuse MPI initialization file if it exists; else create a new one.
      pythiaColl.readString("MultipartonInteractions:reuseInit = 3");
      pythiaColl.readString("MultipartonInteractions:initFile = main183.mpi");
      // Initialize.
      pythiaColl.init();

      // 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) {

        // Four-momentum of incoming initiator.
        Configuration& config = configurations[iCase];
        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 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;

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

          // Low energy hadrons should not interact with medium.
          // Decay non-hadrons or low-energy ones if decay happens above ground.
          if (!hadNow.isHadron() || hadNow.e() - hadNow.m() < config.eKinMin) {
            if (vDec.pz() > 0.) pythiaMain.moreDecays(iHad);
            continue;
          }

          // Invariant mass of particle with a p/n nucleon in atmosphere.
          int idNow     = hadNow.id();
          Vec4 pNow     = hadNow.p();
          double mNow   = hadNow.m();
          double eCMNow = (pNow + Vec4(0, 0, 0, mp)).mCalc();

          // Get hadron-nucleon cross section.
          double sigmaNow = pythiaColl.getSigmaTotal(
            idNow, 2212, eCMNow, mNow, mp);

          // If the cross section vanishes, decay is the only option.
          if (sigmaNow <= 0.) {
            if (vDec.pz() > 0.) pythiaMain.moreDecays(iHad);
            continue;
          }

          // Average number of hadron-nucleon collisions in a
          // hadron-nitrogen one.
          double nCollAvg = (sigmaNow < 31.) ? 1. + 0.017 * sigmaNow
                          : 1.2 + 0.0105 * sigmaNow;
          double probMore = 1. - 1. / nCollAvg;

          // Medium density is expressed in terms of nucleons per volume,
          // so if collisions are clustered to nuclei then sigma must be
          // compensated.
          if (config.doHeavyIon) sigmaNow /= nCollAvg;

          // Calculate potential interaction vertex, depending on medium.
          Vec4 vInt( 0., 0., -1., 0.);
          Vec4 dirNow = pNow / pNow.pAbs();
          // 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. && vDec.pz() < 0.) continue;

          // Do decay if that happens first.
          if (vDec.pz() > vInt.pz()) {
            pythiaMain.moreDecays(iHad);
            continue;
          }

          // Set up for collisions on a nucleus.
          int np = 7;
          int nn = 7;
          int sizeOld = 0;
          int sizeNew = 0;
          double probSD = 0.3;

          // Loop over varying number of hit nucleons in target nucleus.
          for (int iColl = 1; iColl < 10; ++iColl) {
            if (!config.doHeavyIon && iColl == 2) break;
            if (iColl > 1 && rndm.flat() > probMore) break;

            // Pick incoming projectile: trivial for first subcollision, else ...
            int iProj = iHad;
            int procType = 0;

            // ... find highest-pLongitudinal particle from latest subcollision.
            if (iColl > 1) {
              iProj = 0;
              double pMax = 0.;
              for (int i = sizeOld; i < sizeNew; ++i)
              if ( eventMain[i].isFinal() && eventMain[i].isHadron()) {
                double pp = dot3(dirNow, eventMain[i].p());
                if (pp > pMax) {
                  iProj = i;
                  pMax  = pp;
                }
              }

              // No further subcollision if no particle with enough energy.
              if ( iProj == 0 || eventMain[iProj].e() - eventMain[iProj].m()
                < config.eKinMin) break;

              // Choose process; only SD or ND at perturbative energies.
              double eCMSub = (eventMain[iProj].p() + Vec4(0, 0, 0, mp)).mCalc();
              if (eCMSub > 10.) procType = (rndm.flat() < probSD) ? 4 : 1;
            }

            // Pick one p or n from target.
            int idProj = eventMain[iProj].id();
            bool doProton = rndm.flat() < (np / double(np + nn));
            if (doProton) np -= 1;
            else          nn -= 1;
            int idNuc = (doProton) ? 2212 : 2112;

            // Perform the projectile-nucleon subcollision.
            pythiaColl.setBeamIDs(idProj, idNuc);
            pythiaColl.setKinematics(eventMain[iProj].p(), Vec4());
            pythiaColl.next(procType);

            // Insert target nucleon. Mothers are (0,iProj) to mark who it
            // interacted with. Always use proton mass for simplicity.
            int statusNuc = (iColl == 1) ? -181 : -182;
            int iNuc = eventMain.append( idNuc, statusNuc, 0, iProj, 0, 0, 0, 0,
              0., 0., 0., mp, mp);
            eventMain[iNuc].vProdAdd(vInt);

            // Insert secondary produced particles (but skip intermediate
            // partons) into main event record and shift to correct
            // production vertex.
            sizeOld = eventMain.size();
            for (int iSub = 3; iSub < eventColl.size(); ++iSub) {
              if (!eventColl[iSub].isFinal()) continue;
              int iNew = eventMain.append(eventColl[iSub]);
              eventMain[iNew].mothers(iNuc, iProj);
              eventMain[iNew].vProdAdd(vInt);
            }
            sizeNew = eventMain.size();

            // Update daughters of colliding hadrons and other history.
            eventMain[iProj].daughters(sizeOld, sizeNew - 1);
            eventMain[iNuc].daughters(sizeOld, sizeNew - 1);
            eventMain[iProj].statusNeg();
            double dTau = (iColl == 1) ? (vInt.e() - eventMain[iHad].tProd())
              * eventMain[iHad].m() / eventMain[iHad].e() : 0.;
            eventMain[iProj].tau(dTau);

          // End of loop over interactions in a nucleus.
          }

        // 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.
      pythiaMain.stat();
      pythiaColl.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("plot183");
      plt.frame("fig183", "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(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(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(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(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(true);

    }