main483
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// main483.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.
// 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.
// Optionally it can now use Angantyr instead of the above model.
// Warning: Angantyr hadron-nucleus cross sections are not available
// on the fly, so the approach developed for PythiaCascade is used instead.
// There is a mismatch, however, in that Angantyr does not simulate elastic
// scatterings, while PythiaCascade does, so some fudge is involved.
// Also note that Angantyr cannot go as low in collision energy as
// PythiaCascade can, so for comparisons the former sets eCMMin.
// Reminder: for vertex Vec4 the components are labelled (px, py, pz, e),
// but actually represent (x, y, z, t) values.
#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.
// Warning: note that eCMMin later on is a stricter cut by default.
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() {
// Option to use Angantyr for hadron-nucleus collisions instead of default.
bool useAngantyr = true;
// 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;
// Minimal hadron-hadron collision CM-frame energy allowed in the cascade.
// Must be at least 10 GeV for Angantyr, or else it will not work properly.
// For the default model one can go much lower, as given by eKinMin.
bool matchAngantyr = true;
double eCMMin = (useAngantyr || matchAngantyr) ? 10.5 : 0.;
// Set maximum size on the event record, to limit runaway code.
int maxSize = 2000000;
// 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");
// If pythiaMain fails to initialize, exit with error.
if (!pythiaMain.init()) return 1;
// 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.");
// 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");
// Default cascade model, from the article cited at the top.
if (!useAngantyr) {
// Must use the soft and low-energy QCD processes.
pythiaColl.readString("SoftQCD:all = on");
pythiaColl.readString("LowEnergyQCD:all = on");
// Reuse MPI initialization file if it exists; else create a new one.
pythiaColl.readString("MultipartonInteractions:reuseInit = 3");
pythiaColl.readString("MultipartonInteractions:initFile = main483.mpi");
// Angantyr model, still not fully validated.
} else {
// Enable Angantyr.
pythiaColl.readString("HeavyIon:mode = 2");
// Unit weight needed in cascade.
pythiaColl.readString("HeavyIon:forceUnitWeight = on");
// Reuse MPI and cross sections initialization files.
// If they don't exist, you can generate them by running main424.
pythiaColl.readFile("main424.cmnd");
}
// If pythiaColl fails to initialize, exit with error.
if (!pythiaColl.init()) return 1;
// Book histograms and some other statistics..
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);
}
int nAccCol[4] = {0,0,0,0}, nRejCol[4] = {0,0,0,0}, nErrCol[4] = {0,0,0,0};
int nAccBeam[4] = {0,0,0,0}, nRejBeam[4] = {0,0,0,0};
bool outcome;
// Begin loops over configuration 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. Invariant mass with a p/n nucleon at rest.
int idNow = hadNow.id();
Vec4 pNow = hadNow.p();
double mNow = hadNow.m();
double eNow = hadNow.e();
bool mustDecayNow = false;
double eCMNow = (pNow + Vec4(0, 0, 0, mp)).mCalc();
// 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
|| eCMNow < eCMMin) {
if (canDecayNow) mustDecayNow = true;
else continue;
}
// 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 (canDecayNow) mustDecayNow = true;
else continue;
}
// Average number of hadron-nucleon collisions in a
// hadron-nitrogen one. Slightly updated relative to article.
double nCollAvg = (sigmaNow < 20.) ? 1. + 0.0205 * sigmaNow
: 1.20 + 0.0105 * sigmaNow;
double probMore = 1. - 1. / nCollAvg;
// Medium density is in terms of nucleons per volume, so if collisions
// are clustered to nuclei then sigma must be corrected.
if (config.doHeavyIon) sigmaNow /= nCollAvg;
// Ad hoc cross section reduction from excluding elastic collisions,
// since Angantyr does not handle these.
if (useAngantyr) sigmaNow *= 0.9;
// 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;
}
// Perform the decay if it happens first, and then done.
// A failed decay could cause an unintended punch-through.
if (mustDecayNow) {
pythiaMain.moreDecays(iHad);
continue;
}
// Common variables.
int sizeOld = 0;
int sizeNew = 0;
// Use default model to perform an interaction if it happens first.
if (!useAngantyr) {
// Set up for collisions on a p or a nucleus.
int np = 7;
int nn = 7;
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.
if ( pythiaColl.setBeamIDs(idProj, idNuc) &&
pythiaColl.setKinematics(eventMain[iProj].p(), Vec4()) ) {
++nAccBeam[iCase];
} else {
++nRejBeam[iCase];
continue;
}
outcome = pythiaColl.next(procType);
if (outcome) ++nAccCol[iCase];
else ++nRejCol[iCase];
// 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()) {
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.
}
// Use the Angantyr model to perform an interaction if it happens first.
} else {
// Set up for collisions on a p or a nucleus.
int idTarg = (iCase == 0) ? 2212 : 1000070140;
if ( pythiaColl.setBeamIDs(idNow, idTarg) &&
pythiaColl.setKinematics(pNow, Vec4(0., 0., 0., 0.938)) ) {
++nAccBeam[iCase];
} else {
++nRejBeam[iCase];
continue;
}
// Simulate interaction. Skip particle if failure, which
// could lead to unintended punch-through of a particle.
outcome = pythiaColl.next();
if (outcome) ++nAccCol[iCase];
else ++nRejCol[iCase];
if (!outcome) continue;
// Append target.
int iTarg = eventMain.append(idTarg, -181, iHad, iHad, 0, 0, 0, 0,
0., 0., 0., mp, mp);
eventMain[iTarg].vProdAdd(vInt);
// Copy final-state particles.
sizeOld = eventMain.size();
for (int iSub = 3; iSub < eventColl.size(); ++iSub)
if (eventColl[iSub].isFinal()) {
int iNew = eventMain.append(eventColl[iSub]);
eventMain[iNew].mothers(iHad, iTarg);
eventMain[iNew].vProdAdd(vInt);
}
sizeNew = eventMain.size();
// Update daughters of the interacting particles.
eventMain[iTarg].daughters(sizeOld, sizeNew - 1);
eventMain[iHad].daughters(sizeOld, sizeNew - 1);
eventMain[iHad].statusNeg();
double dTau = ( vInt.e() - eventMain[iHad].tProd() ) * mNow / eNow;
eventMain[iHad].tau( dTau);
// End of default or Angantyr model for a hadron-nucleus interaction.
}
// Stop generation if the event record is 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.
Vec4 pSumFinal;
for (Particle& h : eventMain) {
if (h.isFinal()) pSumFinal += h.p();
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.);
}
}
// Check for three-momentum conservation (but energy broken by atmosphere).
double pxyzErr = abs(pSumFinal[1] - pxPri) + abs(pSumFinal[2] - pyPri)
+ abs(pSumFinal[3] + pzPri);
if (pxyzErr > 1e-4 * pPri) ++nErrCol[iCase];
// End loops over events and cases.
}
// Print statistics, mainly for errors.
cout << "\n Statistics from PythiaMain: " << endl;
pythiaMain.stat();
cout << "\n Statistics from PythiaColl: " << endl;
pythiaColl.stat();
cout << "\n Number of accepted beam/target id/energy: " << nAccCol[0] << " "
<< nAccCol[1] << " " << nAccCol[2] << " " << nAccCol[3] ;
cout << "\n Number of rejected beam/target id/energy: " << nRejCol[0] << " "
<< nRejCol[1] << " " << nRejCol[2] << " " << nRejCol[3] ;
cout << "\n Number of accepted subcollisions : " << nAccCol[0] << " "
<< nAccCol[1] << " " << nAccCol[2] << " " << nAccCol[3] ;
cout << "\n Number of rejected subcollisions : " << nRejCol[0] << " "
<< nRejCol[1] << " " << nRejCol[2] << " " << nRejCol[3] ;
cout << "\n Number of non-conserving events : " << nErrCol[0] << " "
<< nErrCol[1] << " " << nErrCol[2] << " " << nErrCol[3] << endl;
// 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("plot483");
plt.frame("fig483", "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, 0.01, 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);
}