Rivet analyses
title: H1_1996_I422230
Charged particle multiplicities in deep inelastic scattering at HERA
Experiment: H1 (HERA)
Inspire ID: 422230
Status: VALIDATED
Authors: - Ariadna Leon - Hannes Jung
References: - Z.Phys.C 72 (1996) 573-592 - DOI: 10.1007/s002880050280,10.1007/BF02909189 - arXiv: hep-ex/9608011 - DESY-96-160
Beams: e+ p+, p+ e+
Beam energies: (27.5, 820.0); (820.0, 27.5)GeV
Run details: - validation with 3000001 events generated RAPGAP33, 26.7x820 GeV, Q2>2, 0.01 < y <0.95, IPRO=12, pt2cut=9, mixing with O(alphas) process, Nf_QCDC=4, NFLA=5
Using the H1 detector at HERA, charged particle multiplicity distributions in deep inelastic ep scattering have been measured over a large kinematical region. The evolution with W and Q2 of the multiplicity distribution and of the multiplicity moments in pseudorapidity domains of varying size is studied in the current fragmentation region of the hadronic centre-of-mass frame. Data on multiplicity as well as the various moments of the distribution are given in a variety of psuedorapidity regions. The moments are the generalised dispersions (D), the factorial moments (R), the Muller moments (K) and the C factors (C).
Source code:H1_1996_I422230.cc
```c++ // -- C++ --
include "Rivet/Analysis.hh"
include "Rivet/Projections/ChargedFinalState.hh"
include "Rivet/Projections/DISKinematics.hh"
include "Rivet/Projections/FastJets.hh"
include "Rivet/Projections/FinalState.hh"
namespace Rivet {
/// @brief Charged particle multiplicities in deep inelastic scattering at HERA (H1) class H1_1996_I422230 : public Analysis { public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(H1_1996_I422230);
/// @name Analysis methods
///@{
/// Book histograms and initialise projections before the run
void init() {
// Initialise and register projections
const DISLepton disl;
declare(disl, "Lepton");
declare(DISKinematics(), "Kinematics");
// The basic final-state projection:
// all final-state particles within
// the given eta acceptance
const FinalState fs;
declare(fs, "FS");
const ChargedFinalState cfs(disl.remainingFinalState());
declare(cfs, "CFS");
//binned histograms to count for the multiplicity
for (size_t ix = 0; ix < 4; ++ix) {
book(_Nevt_after_cuts[ix], "TMP/Nevt_after_cuts" + to_string(ix));
}
const vector<double> WEdges{80., 115, 150., 185., 220.};
book(_g["mult1"], WEdges);
book(_g["mult2"], WEdges);
book(_g["mult3"], WEdges);
book(_g["mult4"], WEdges);
book(_g["mult_all"], WEdges);
book(_g["mult10_all"], WEdges);
book(_g["mult11_all"], WEdges);
book(_g["mult12_all"], WEdges);
for (size_t iW = 0; iW < _g["mult1"]->numBins(); ++iW) {
book(_g["mult1"]->bin(iW + 1), iW + 1, 1, 1);
book(_g["mult2"]->bin(iW + 1), iW + 1, 1, 2);
book(_g["mult3"]->bin(iW + 1), iW + 1, 1, 3);
book(_g["mult4"]->bin(iW + 1), iW + 1, 1, 4);
const auto& ref = refData<YODA::BinnedEstimate<int>>(4, 1, 4);
book(_g["mult_all"]->bin(iW + 1), "TMP/dummy" + to_string(iW), ref);
book(_g["mult10_all"]->bin(iW + 1), "TMP/dummy1" + to_string(iW), ref);
book(_g["mult11_all"]->bin(iW + 1), "TMP/dummy2" + to_string(iW), ref);
book(_g["mult12_all"]->bin(iW + 1), "TMP/dummy3" + to_string(iW), ref);
}
//histograms for the statistical moments and the mean
book(_e["mean0"], 5, 1, 1);
book(_e["D2_0"], 5, 1, 2);
book(_e["D3_0"], 5, 1, 3);
book(_e["D4_0"], 5, 1, 4);
book(_e["C2_0"], 5, 1, 5);
book(_e["C3_0"], 5, 1, 6);
book(_e["C4_0"], 5, 1, 7);
book(_e["R2_0"], 5, 1, 8);
book(_e["R3_0"], 5, 1, 9);
book(_e["mean12"], 6, 1, 1);
book(_e["D2_12"], 6, 1, 2);
book(_e["D3_12"], 6, 1, 3);
book(_e["D4_12"], 6, 1, 4);
book(_e["C2_12"], 6, 1, 5);
book(_e["C3_12"], 6, 1, 6);
book(_e["C4_12"], 6, 1, 7);
book(_e["R2_12"], 6, 1, 8);
book(_e["R3_12"], 6, 1, 9);
book(_e["K3_12"], 6, 1, 10);
book(_e["mean13"], 7, 1, 1);
book(_e["D2_13"], 7, 1, 2);
book(_e["D3_13"], 7, 1, 3);
book(_e["D4_13"], 7, 1, 4);
book(_e["C2_13"], 7, 1, 5);
book(_e["C3_13"], 7, 1, 6);
book(_e["C4_13"], 7, 1, 7);
book(_e["R2_13"], 7, 1, 8);
book(_e["R3_13"], 7, 1, 9);
book(_e["K3_13"], 7, 1, 10);
book(_e["mean14"], 8, 1, 1);
book(_e["D2_14"], 8, 1, 2);
book(_e["D3_14"], 8, 1, 3);
book(_e["D4_14"], 8, 1, 4);
book(_e["C2_14"], 8, 1, 5);
book(_e["C3_14"], 8, 1, 6);
book(_e["C4_14"], 8, 1, 7);
book(_e["R2_14"], 8, 1, 8);
book(_e["R3_14"], 8, 1, 9);
book(_e["mean15"], 9, 1, 1);
book(_e["D2_15"], 9, 1, 2);
book(_e["D3_15"], 9, 1, 3);
book(_e["D4_15"], 9, 1, 4);
book(_e["C2_15"], 9, 1, 5);
book(_e["C3_15"], 9, 1, 6);
book(_e["C4_15"], 9, 1, 7);
book(_e["R2_15"], 9, 1, 8);
book(_e["R3_15"], 9, 1, 9);
book(_e["mean23"], 10, 1, 1);
book(_e["D2_23"], 10, 1, 2);
book(_e["D3_23"], 10, 1, 3);
book(_e["D4_23"], 10, 1, 4);
book(_e["C2_23"], 10, 1, 5);
book(_e["C3_23"], 10, 1, 6);
book(_e["C4_23"], 10, 1, 7);
book(_e["R2_23"], 10, 1, 8);
book(_e["R3_23"], 10, 1, 9);
book(_e["K3_23"], 10, 1, 10);
book(_e["mean34"], 11, 1, 1);
book(_e["D2_34"], 11, 1, 2);
book(_e["D3_34"], 11, 1, 3);
book(_e["D4_34"], 11, 1, 4);
book(_e["C2_34"], 11, 1, 5);
book(_e["C3_34"], 11, 1, 6);
book(_e["C4_34"], 11, 1, 7);
book(_e["R2_34"], 11, 1, 8);
book(_e["R3_34"], 11, 1, 9);
book(_e["K3_34"], 11, 1, 10);
book(_e["mean45"], 12, 1, 1);
book(_e["D2_45"], 12, 1, 2);
book(_e["D3_45"], 12, 1, 3);
book(_e["D4_45"], 12, 1, 4);
book(_e["C2_45"], 12, 1, 5);
book(_e["C3_45"], 12, 1, 6);
book(_e["C4_45"], 12, 1, 7);
book(_e["R2_45"], 12, 1, 8);
book(_e["R3_45"], 12, 1, 9);
book(_e["K3_45"], 12, 1, 10);
}
/// Perform the per-event analysis
void analyze(const Event& event) {
//apply the final state of all particles and the one for only charged particles
const FinalState& fs = apply<FinalState>(event, "FS");
const size_t numParticles = fs.particles().size();
const ChargedFinalState& cfs = apply<ChargedFinalState>(event, "CFS");
const Particles& particles = cfs.particles();
//because it does not make sense to have a collision with the numparticles is less than two,we use the vetoEvent so that if there is an event like this it does not run the analysis and goes to the next one
if (numParticles < 2) {
MSG_DEBUG("Failed leptonic cut");
vetoEvent;
}
//apply DIS kinematics in the event
const DISKinematics& dk = apply<DISKinematics>(event, "Kinematics");
//const DISLepton& dl = apply<DISLepton>(event,"Lepton");
//get the DIS Kinematics but not in a loop because they are variables that descrube the type of event not the particles
double Q2 = dk.Q2();
double W2 = dk.W2();
double W = std::sqrt(W2);
bool cut1 = W < 220. && W > 80.;
if (!cut1) vetoEvent;
bool cut = Q2 < 1000. && Q2 > 10. && W > 80. && W < 220.;
if (!cut) vetoEvent;
double Efwd = 0.;
for (size_t ip1 = 0; ip1 < particles.size(); ++ip1) {
const Particle& p = particles[ip1];
double theta = p.theta() / degree;
if (inRange(theta, 4.4, 15.)) {
Efwd = Efwd + p.E();
}
}
bool cut_fwd = Efwd > 0.5 && dk.beamLepton().E() > 12.;
if (!cut_fwd) vetoEvent;
const size_t idx = _g["mult1"]->binAt(W).index();
if (0 < idx && idx < 5) {
_Nevt_after_cuts[idx - 1]->fill();
}
//boost to the hadronic centre of mass frame
const LorentzTransform hcmboost = dk.boostHCM();
int kall = 0.;
int k1 = 0.;
int k2 = 0.;
int k3 = 0.;
int k4 = 0.;
int k10 = 0.;
int k11 = 0.;
int k12 = 0.;
for (size_t ip1 = 0; ip1 < particles.size(); ++ip1) {
const Particle& p = particles[ip1];
const FourMomentum hcmMom = hcmboost.transform(p.momentum());
const double etahcm_char = hcmMom.eta();
if (etahcm_char > 0.) ++kall;
if (etahcm_char > 1. && etahcm_char < 2.) {
++k1;
}
if (etahcm_char > 1. && etahcm_char < 3.) {
++k2;
}
if (etahcm_char > 1. && etahcm_char < 4.) {
++k3;
}
if (etahcm_char > 1. && etahcm_char < 5.) {
++k4;
}
if (etahcm_char > 2. && etahcm_char < 3.) {
++k10;
}
if (etahcm_char > 3. && etahcm_char < 4.) {
++k11;
}
if (etahcm_char > 4. && etahcm_char < 5.) {
++k12;
}
}
_g["mult_all"]->fill(W, kall);
_g["mult10_all"]->fill(W, k10);
_g["mult11_all"]->fill(W, k11);
_g["mult12_all"]->fill(W, k12);
_g["mult1"]->fill(W, k1);
_g["mult2"]->fill(W, k2);
_g["mult3"]->fill(W, k3);
_g["mult4"]->fill(W, k4);
}
/// Normalise histograms etc., after the run
void finalize() {
unsigned int iq;
double mean, dispersion, cq, R2, R3, K3;
for (auto& histo : _g["mult_all"]->bins()) {
iq = 2;
size_t iW = histo.index();
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
// just to have some values, needs to be corrected
_e["mean0"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_0"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_0"]->bin(iW).set(cq, cq / mean);
_e["R2_0"]->bin(iW).set(R2, R2 / mean);
_e["R3_0"]->bin(iW).set(R3, R3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_0"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_0"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_0"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_0"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult1"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean12"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_12"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_12"]->bin(iW).set(cq, cq / mean);
_e["R2_12"]->bin(iW).set(R2, R2 / mean);
_e["R3_12"]->bin(iW).set(R3, R3 / mean);
_e["K3_12"]->bin(iW).set(K3, K3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_12"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_12"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_12"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_12"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult2"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean13"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_13"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_13"]->bin(iW).set(cq, cq / mean);
_e["R2_13"]->bin(iW).set(R2, R2 / mean);
_e["R3_13"]->bin(iW).set(R3, R3 / mean);
_e["K3_13"]->bin(iW).set(K3, K3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_13"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_13"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_13"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_13"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult3"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean14"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_14"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_14"]->bin(iW).set(cq, cq / mean);
_e["R2_14"]->bin(iW).set(R2, R2 / mean);
_e["R3_14"]->bin(iW).set(R3, R3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_14"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_14"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_14"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_14"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult4"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean15"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_15"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_15"]->bin(iW).set(cq, cq / mean);
_e["R2_15"]->bin(iW).set(R2, R2 / mean);
_e["R3_15"]->bin(iW).set(R3, R3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_15"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_15"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_15"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_15"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult10_all"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean23"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_23"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_23"]->bin(iW).set(cq, cq / mean);
_e["R2_23"]->bin(iW).set(R2, R2 / mean);
_e["R3_23"]->bin(iW).set(R3, R3 / mean);
_e["K3_23"]->bin(iW).set(K3, K3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_23"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_23"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_23"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_23"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult11_all"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean34"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_34"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_34"]->bin(iW).set(cq, cq / mean);
_e["R2_34"]->bin(iW).set(R2, R2 / mean);
_e["R3_34"]->bin(iW).set(R3, R3 / mean);
_e["K3_34"]->bin(iW).set(K3, K3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_34"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_34"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_34"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_34"]->bin(iW).set(cq, cq / mean);
}
mean = 0.;
dispersion = 0.;
cq = 0.;
R2 = 0;
R3 = 0.;
K3 = 0.;
for (auto& histo : _g["mult12_all"]->bins()) {
// use scale to get Prob in %, and use counter to count events after cuts
size_t iW = histo.index();
scale(histo, 100.0 / *_Nevt_after_cuts[iW - 1]);
//
iq = 2;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["mean45"]->bin(iW).set(mean, 0.5 * dispersion);
_e["D2_45"]->bin(iW).set(dispersion, dispersion / mean);
_e["C2_45"]->bin(iW).set(cq, cq / mean);
_e["R2_45"]->bin(iW).set(R2, R2 / mean);
_e["R3_45"]->bin(iW).set(R3, R3 / mean);
_e["K3_45"]->bin(iW).set(K3, K3 / mean);
iq = 3;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D3_45"]->bin(iW).set(dispersion, dispersion / mean);
_e["C3_45"]->bin(iW).set(cq, cq / mean);
iq = 4;
dispersion = 0;
cq = 0;
_histo_to_moments(histo, iq, mean, dispersion, cq, R2, R3, K3);
_e["D4_45"]->bin(iW).set(dispersion, dispersion / mean);
_e["C4_45"]->bin(iW).set(cq, cq / mean);
}
}
inline void _histo_to_moments(const BinnedHistoPtr<int>& histo_input,
unsigned int iq,
double& mean,
double& dispersion,
double& cq,
double& R2,
double& R3,
double& K3) {
double mysumWX = 0.;
double mysumW = 0.;
if (histo_input->effNumEntries() == 0 || histo_input->sumW() == 0) {
mean = dispersion = cq = R2 = R3 = K3 = std::numeric_limits<double>::quiet_NaN();
MSG_WARNING("Requested mean of a distribution with no net fill weights");
}
else {
// loop to calculate mean
for (const auto& b : histo_input->bins()) { // loop over points
mysumWX += b.sumW() * b.xEdge();
mysumW += b.sumW();
}
mean = mysumWX / mysumW;
// loop to calculate dispersion (variance)
double var = 0., c = 0., r2 = 0., r3 = 0.;
for (const auto& b : histo_input->bins()) { // loop over points
const double xval = b.xEdge();
const double weight = b.sumW();
var = var + weight * intpow((xval - mean), iq);
c = c + intpow(xval, iq) * weight;
r2 = r2 + xval * (xval - 1) * weight;
r3 = r3 + xval * (xval - 1) * (xval - 2) * weight;
}
var = var / mysumW;
dispersion = pow(var, 1.0 / (double)iq);
cq = c / (mysumW * intpow(mean, iq));
R2 = r2 / (mysumW * intpow(mean, 2));
R3 = r3 / (mysumW * intpow(mean, 3));
K3 = subtract(R3, 3 * R2 - 2);
}
}
///@}
private:
/// @name Histograms
///@{
map<string, HistoGroupPtr<double, int>> _g;
map<string, Estimate1DPtr> _e;
CounterPtr _Nevt_after_cuts[4];
///@}
};
RIVET_DECLARE_PLUGIN(H1_1996_I422230);
} ```