Rivet analyses
Gluon jet charged multiplicities and fragmentation functions
Experiment: OPAL (LEP)
Inspire ID: 631361
Status: VALIDATED
Authors: - Daniel Reichelt
References: - Phys. Rev. D69, 032002,2004 - hep-ex/0310048
Beams: e+ e-
Beam energies: (5.2, 5.2); (6.0, 6.0); (7.0, 7.0); (8.4, 8.4); (10.9, 10.9); (14.2, 14.2); (17.7, 17.7); (45.6, 45.6)GeV
Run details: - The fictional e+e− → gg process
Measurement of gluon jet properties using the jet boost algorithm, a technique to select unbiased samples of gluon jets in e+e− annihilation, i.e. gluon jets free of biases introduced by event selection or jet finding criteria. Two modes are provided, the prefer option is to produce the fictional $e+e-g g $ process to be used due to the corrections applied to the data, PROCESS=GG. The original analysis technique to extract gluon jets from hadronic e+e− events using e+e− → qq̄ events, PROCESS=QQ, is also provided but cannot be used for tuning as the data has been corrected for impurities, however it is still useful qualitatively in order to check the properties of gluon jets in the original way in which there were measured rather than using a fictitious process.
Source
code:OPAL_2004_I631361.cc
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/ChargedFinalState.hh"
#include "Rivet/Projections/FastJets.hh"
#include "Rivet/Projections/HadronicFinalState.hh"
#include "fastjet/JetDefinition.hh"
namespace fastjet {
class P_scheme : public JetDefinition::Recombiner {
public:
std::string description() const {return "";}
void recombine(const PseudoJet & pa, const PseudoJet & pb,
PseudoJet & pab) const {
PseudoJet tmp = pa + pb;
double E = sqrt(tmp.px()*tmp.px() + tmp.py()*tmp.py() + tmp.pz()*tmp.pz());
pab.reset_momentum(tmp.px(), tmp.py(), tmp.pz(), E);
}
void preprocess(PseudoJet & p) const {
double E = sqrt(p.px()*p.px() + p.py()*p.py() + p.pz()*p.pz());
p.reset_momentum(p.px(), p.py(), p.pz(), E);
}
~P_scheme() { }
};
}
namespace Rivet {
class OPAL_2004_I631361 : public Analysis {
public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(OPAL_2004_I631361);
/// @name Analysis methods
/// @{
void init() {
// Get options from the new option system
_mode = 0;
if ( getOption("PROCESS") == "GG" ) _mode = 0;
if ( getOption("PROCESS") == "QQ" ) _mode = 1;
// projections we need for both cases
const FinalState fs;
declare(fs, "FS");
const ChargedFinalState cfs;
declare(cfs, "CFS");
// additional projections for q qbar
if (_mode==1) {
declare(HadronicFinalState(fs), "HFS");
declare(HadronicFinalState(cfs), "HCFS");
}
// book the histograms
if (_mode==0) {
int ih(0), iy(0);
if (inRange(0.5*sqrtS()/GeV, 5.0, 5.5)) {
ih = 1;
iy = 1;
} else if (inRange(0.5*sqrtS()/GeV, 5.5, 6.5)) {
ih = 1;
iy = 2;
} else if (inRange(0.5*sqrtS()/GeV, 6.5, 7.5)) {
ih = 1;
iy = 3;
} else if (inRange(0.5*sqrtS()/GeV, 7.5, 9.5)) {
ih = 2;
iy = 1;
} else if (inRange(0.5*sqrtS()/GeV, 9.5, 13.0)) {
ih = 2;
iy = 2;
} else if (inRange(0.5*sqrtS()/GeV, 13.0, 16.0)) {
ih = 3;
iy = 1;
} else if (inRange(0.5*sqrtS()/GeV, 16.0, 20.0)) {
ih = 3;
iy = 2;
}
if (!ih) MSG_WARNING("Option \"PROCESS=GG\" not compatible with this beam energy!");
assert(ih>0);
book(_h_chMult_gg, ih, 1, iy);
if (ih==3) book(_h_chFragFunc_gg, 5,1,iy);
else _h_chFragFunc_gg = nullptr;
book(_sumW,"/TMP/sumW");
}
else {
book(_h_chMult_qq, { 5.0, 5.5, 6.5, 7.5, 9.5, 13.0, 16.0, 20.0 },
{ "d01-x01-y01", "d01-x01-y02", "d01-x01-y03", "d02-x01-y01",
"d02-x01-y02", "d03-x01-y01", "d03-x01-y02" });
book(_h_chFragFunc_qq, { 13., 16., 20. }, { "d05-x01-y01", "d05-x01-y02" });
_sumWEbin.resize(7);
for (size_t i = 0; i < 7; ++i) {
book(_sumWEbin[i], "/TMP/sumWEbin" + to_string(i));
}
}
}
/// Perform the per-event analysis
void analyze(const Event& event) {
// gg mode
if (_mode==0) {
// find the initial gluons
Particles initial;
for (ConstGenParticlePtr p : HepMCUtils::particles(event.genEvent())) {
ConstGenVertexPtr pv = p->production_vertex();
const PdgId pid = p->pdg_id();
if(pid!=21) continue;
bool passed = false;
for (ConstGenParticlePtr pp : HepMCUtils::particles(pv, Relatives::PARENTS)) {
const PdgId ppid = abs(pp->pdg_id());
passed = (ppid == PID::ELECTRON || ppid == PID::HIGGS || ppid == PID::ZBOSON || ppid == PID::GAMMA);
if (passed) break;
}
if (passed) initial.push_back(Particle(*p));
}
if (initial.size()!=2) vetoEvent;
// use the direction for the event axis
Vector3 axis = initial[0].momentum().p3().unit();
// fill histograms
const Particles& chps = apply<FinalState>(event, "CFS").particles();
unsigned int nMult[2] = {0,0};
// distribution
for (const Particle& p : chps) {
const double xE = 2.*p.E()/sqrtS();
if (_h_chFragFunc_gg) _h_chFragFunc_gg->fill(xE);
if (p.momentum().p3().dot(axis)>0.) {
++nMult[0];
}
else {
++nMult[1];
}
}
// multiplicities in jet
_h_chMult_gg->fill(nMult[0]);
_h_chMult_gg->fill(nMult[1]);
_sumW->fill();
}
// qqbar mode
else {
// cut on the number of charged particles
const Particles& chParticles = apply<FinalState>(event, "CFS").particles();
if (chParticles.size() < 5) vetoEvent;
// cluster the jets
const Particles& particles = apply<FinalState>(event, "FS").particles();
fastjet::JetDefinition ee_kt_def(fastjet::ee_kt_algorithm, &p_scheme);
PseudoJets pParticles;
for (Particle p : particles) {
PseudoJet temp = p.pseudojet();
if(p.fromBottom()) {
temp.set_user_index(5);
}
pParticles.push_back(temp);
}
fastjet::ClusterSequence cluster(pParticles, ee_kt_def);
// rescale energys to just keep the directions of the jets
// and keep track of b tags
PseudoJets pJets = sorted_by_E(cluster.exclusive_jets_up_to(3));
if (pJets.size() < 3) vetoEvent;
array<Vector3, 3> dirs;
for (int i=0; i<3; i++) {
dirs[i] = Vector3(pJets[i].px(),pJets[i].py(),pJets[i].pz()).unit();
}
array<bool, 3> bTagged;
Jets jets;
for (int i=0; i<3; i++) {
double Ejet = sqrtS()*sin(angle(dirs[(i+1)%3],dirs[(i+2)%3])) /
(sin(angle(dirs[i],dirs[(i+1)%3])) + sin(angle(dirs[i],dirs[(i+2)%3])) + sin(angle(dirs[(i+1)%3],dirs[(i+2)%3])));
jets.push_back(FourMomentum(Ejet,Ejet*dirs[i].x(),Ejet*dirs[i].y(),Ejet*dirs[i].z()));
bTagged[i] = false;
for (PseudoJet particle : pJets[i].constituents()) {
if (particle.user_index() > 1 and !bTagged[i]) {
bTagged[i] = true;
}
}
}
int QUARK1 = 0, QUARK2 = 1, GLUON = 2;
if (jets[QUARK2].E() > jets[QUARK1].E()) swap(QUARK1, QUARK2);
if (jets[GLUON].E() > jets[QUARK1].E()) swap(QUARK1, GLUON);
if (!bTagged[QUARK2]) {
if (!bTagged[GLUON]) vetoEvent;
else swap(QUARK2, GLUON);
}
if (bTagged[GLUON]) vetoEvent;
// exclude collinear or soft jets
double k1 = jets[QUARK1].E()*min(angle(jets[QUARK1].momentum(),jets[QUARK2].momentum()),
angle(jets[QUARK1].momentum(),jets[GLUON].momentum()));
double k2 = jets[QUARK2].E()*min(angle(jets[QUARK2].momentum(),jets[QUARK1].momentum()),
angle(jets[QUARK2].momentum(),jets[GLUON].momentum()));
if (k1<8.0*GeV || k2<8.0*GeV) vetoEvent;
double sqg = (jets[QUARK1].momentum()+jets[GLUON].momentum()).mass2();
double sgq = (jets[QUARK2].momentum()+jets[GLUON].momentum()).mass2();
double s = (jets[QUARK1].momentum()+jets[QUARK2].momentum()+jets[GLUON].momentum()).mass2();
double Eg = 0.5*sqrt(sqg*sgq/s);
if (Eg < 5.0 || Eg > 46.) { vetoEvent; }
else if (Eg > 9.5) {
//requirements for experimental reconstructability raise as energy raises
if(!bTagged[QUARK1]) {
vetoEvent;
}
}
// all cuts applied, increment sum of weights
_sumWEbin[getEbin(Eg)]->fill();
// transform to frame with event in y-z and glue jet in z direction
Matrix3 glueTOz(jets[GLUON].momentum().vector3(), Vector3(0,0,1));
Vector3 transQuark = glueTOz*jets[QUARK2].momentum().vector3();
Matrix3 quarksTOyz(Vector3(transQuark.x(), transQuark.y(), 0), Vector3(0,1,0));
// work out transformation to symmetric frame
array<double, 3> x_cm;
array<double, 3> x_cm_y;
array<double, 3> x_cm_z;
array<double, 3> x_pr;
for (int i=0; i<3; i++) {
x_cm[i] = 2*jets[i].E()/sqrt(s);
Vector3 p_transf = quarksTOyz*glueTOz*jets[i].p3();
x_cm_y[i] = 2*p_transf.y()/sqrt(s);
x_cm_z[i] = 2*p_transf.z()/sqrt(s);
}
x_pr[GLUON] = sqrt(4*(1-x_cm[QUARK1])*(1-x_cm[QUARK2])/(3+x_cm[GLUON]));
x_pr[QUARK1] = x_pr[GLUON]/(1-x_cm[QUARK1]);
x_pr[QUARK2] = x_pr[GLUON]/(1-x_cm[QUARK2]);
double gamma = (x_pr[QUARK1] + x_pr[GLUON] + x_pr[QUARK2])/2;
double beta_z = x_pr[GLUON]/(gamma*x_cm[GLUON]) - 1;
double beta_y = (x_pr[QUARK2]/gamma - x_cm[QUARK2] - beta_z*x_cm_z[QUARK2])/x_cm_y[QUARK2];
LorentzTransform toSymmetric = LorentzTransform::mkObjTransformFromBeta(Vector3(0.,beta_y,beta_z)).
postMult(quarksTOyz*glueTOz);
FourMomentum transGlue = toSymmetric.transform(jets[GLUON].momentum());
double cutAngle = angle(toSymmetric.transform(jets[QUARK2].momentum()), transGlue)/2;
int nCh = 0;
for (const Particle& chP : chParticles ) {
FourMomentum pSymmFrame = toSymmetric.transform(FourMomentum(chP.p3().mod(), chP.px(), chP.py(), chP.pz()));
if(angle(pSymmFrame, transGlue) < cutAngle) {
_h_chFragFunc_qq->fill(Eg, pSymmFrame.E()*sin(cutAngle)/Eg);
nCh++;
}
}
_h_chMult_qq->fill(Eg, nCh);
}
}
/// Normalise histograms etc., after the run
void finalize() {
if (_mode==0) {
normalize(_h_chMult_gg);
if (_h_chFragFunc_gg) scale(_h_chFragFunc_gg, 0.5/(*_sumW));
}
else {
normalize(_h_chMult_qq);
for (auto& b : _h_chFragFunc_qq->bins()) {
const double sf = _sumWEbin[b.index()+4]->val();
if (sf) scale(b, 1./sf);
}
}
}
/// @}
private:
int getEbin(double E_glue) {
int ih = -1;
if (inRange(E_glue/GeV, 5.0, 5.5)) {
ih = 0;
} else if (inRange(E_glue/GeV, 5.5, 6.5)) {
ih = 1;
} else if (inRange(E_glue/GeV, 6.5, 7.5)) {
ih = 2;
} else if (inRange(E_glue/GeV, 7.5, 9.5)) {
ih = 3;
} else if (inRange(E_glue/GeV, 9.5, 13.0)) {
ih = 4;
} else if (inRange(E_glue/GeV, 13.0, 16.0)) {
ih = 5;
} else if (inRange(E_glue/GeV, 16.0, 20.0)) {
ih = 6;
}
assert(ih >= 0);
return ih;
}
private:
// The mode
unsigned int _mode;
/// needed to normalize as normalised is integral = <average no particles>
vector<CounterPtr> _sumWEbin;
CounterPtr _sumW;
// p scheme jet definition
fastjet::P_scheme p_scheme;
/// @name Histograms
/// @{
BinnedHistoPtr<int> _h_chMult_gg;
Histo1DPtr _h_chFragFunc_gg;
HistoGroupPtr<double,int> _h_chMult_qq;
Histo1DGroupPtr _h_chFragFunc_qq;
/// @}
};
RIVET_DECLARE_PLUGIN(OPAL_2004_I631361);
}