CER

N-T

HES

IS-2

013-

427

University of Warsaw

Faculty of Physics

Agnieszka Ilnicka

Student’s book no.: 262431

Comparison of hadron production

in Monte-Carlo models and

experimental data in p+p

interactions at the SPS energies

second cycle degree thesis

field of study Physics

speciality Particle and Nuclear Physics

within Inter-Faculty Individual Studies in Mathematics and Natural

Sciences (MISMaP)

The thesis written under the supervision of

Prof. dr hab. Wojciech Dominik

Institute of Experimental Physics

Section of Particles and Fundamental Interactions

September 2013

Statement of the Supervisor on Submission of the Thesis

I hereby certify that the thesis submitted has been prepared under my supervision

and I declare that it satisfies the requirements of submission in the proceedings for

the award of a degree.

Date Signature of the Supervisor

Statement of the Author(s) on Submission of the Thesis

Aware of legal liability I certify that the thesis submitted has been prepared by

myself and does not include information gathered contrary to the law.

I also declare that the thesis submitted has not been the subject of proceedings

resulting in the award of a university degree.

Furthermore I certify that the submitted version of the thesis is identical with

its attached electronic version.

Date Signature of the Author(s) of the thesis

Summary

The aim of this thesis is the comparison of the particle production in proton-proton

interactions simulated by Monte Carlo (MC) models used in NA61/SHINE collaboration:

EPOS and VENUS with the available experimental data. The analysis of total multiplic-

ities of strange particles (Λ, Λ̄, K0s , K+ and K−) and negatively charged pions showed

that the EPOS model describes better the experimental data. Also the analysis of trans-

verse mass was done, and the inverse slope parameter of transverse mass spectra T were

obtained and compared with existing experimental data. The comparison was the base to

tune to the particle spectra obtained with the MC models. The adjustments were then em-

ployed in analysis of spectra of negatively charged pions, obtained with the data collected

in NA61/SHINE experiment. The methods of application of correction were compared to

choose the best one.

Key words

NA61/SHINE, SPS, EPOS, VENUS, proton-proton interaction, p+p

Area of study (codes according to Erasmus Subject Area Codes List)

13.2 Physics

The title of the thesis in Polish

Porównanie produkcji hadronów w modelach Monte Carlo oraz danych eksperymentalnych

z oddzia lywań proton-proton przy energiach SPSu.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1. NA61/SHINE Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1.1. Physical Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1.2. NA61 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.1.3. Reconstruction of Events . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2. Nuclear-Scattering Models for Monte Carlo Simulations . . . . . . . . . . . 15

1.2.1. Monte Carlo simulations in Particle Physics . . . . . . . . . . . . . . 15

1.2.2. Nuclear Scattering Models: EPOS and VENUS . . . . . . . . . . . . 17

2. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1. Multiplicities of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2. Transverse Mass and T Parameter . . . . . . . . . . . . . . . . . . . . . . . 30

3.3. Tuning of the Particle Spectra from Monte Carlo simulations . . . . . . . . 33

3.4. The h− Corrections: Methods of Application and Inclusion of Particle Ad-

justments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4. Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5

Chapter 1

Introduction

The aim of this thesis is the comparison of hadron production in the Monte Carlo (MC)

simulations and from the reference experimental data. It is then used to construct the

corrections to the data obtained in the experiment NA61/SHINE. In this section will be

presented the overview of the experiment and the use of the Monte Carlo simulations in

the particle physics.

1.1. NA61/SHINE Experiment

The NA61/SHINE (SPS Heavy Ion and Neutrino Experiment) is a fixed-target experiment

located in the North Area of the European Organization for Nuclear Research (CERN)

and is a collaboration of over 150 physicists associated with 27 institutions. The detector

is a large acceptance hadron spectrometer with the time-projection chambers (TPCs) as

the main detectors. The experiment is supplied with the beam from the Super Proton

Synchrotron (SPS) accelerator. The equipment was inherited from the NA49 experiment

and then modified and modernized. The equipment is capable of performing precise mea-

surements of hadron final states and thus may be used not only for its own physical

programme, but also to collect the reference data for other experiments: neutrino and

cosmic ray. In subsequent sections the physical program, detector setup and principles of

reconstruction will be described.

1.1.1. Physical Goals

Ion program: the search of the onset of deconfinement and critical point

The results presented by the NA49 collaboration suggested the existence of the Quark-

Gluon Plasma (QGP) in the early stage after Pb+Pb collision at the high SPS energy

range. This is indicated by rapid change of hadron production properties in this energy

range, as can be seen in plots presented in Figure 1.1. This suggests that the SPS-based

experiment may be of use in a study of the onset of the deconfinement as well as the

critical point of the strongly interacting matter [1, 2]. The onset of deconfinement referes

7

Figure 1.1: NA49 results compiled with the world data [4]: (a) The pion multiplicitydivided by the number of wounded nucleon in the Fermi energy. In the Pb+Pb data isobservable the steepening from the linear dependence present in p+p case. (b) Ratio of thepositive kaon to pion multiplicities versus center-of-mass energy

√s. The sharp maximum

is observed in the Pb+Pb data, lacked in the p+p interaction. (c) The inverse slopeparameter T of transverse mass spectra of positive kaons versus center-of-mass energy. Incase of Pb+Pb interaction the plateau is observed, not present in p+p data.

to the creation of deconfined states of strongly interacting matter (such as quark-gluon

plasma) while critical point is the limit over which not phase transitions occure (see Figure

1.2. The interaction of hadrons at different energies and with different system sizes (the

number of nucleons) enable the exploration of the phase space diagram in the temperature

and the baryonic potential of strongly interacting matter, what is schematically shown in

Figure 1.2. Thus, the NA61/SHINE experiment has a rich ion program: it consists of

collisions within the SPS energy range (at 13, 20, 30, 40, 80 and 158 GeV/c) of protons

and ions: with A around 8 (Be+Be), 30 (Ar+Ca) and 110 (Xe+La). The interactions

occur on targets with a similar atomic mass as the beam.

The energy range available in SPS fits between the energies available in AGS and RHIC

accelerators of the Brookhaven National Laboratory, thus the data obtained by NA61 will

be complementary to the data obtained elsewhere. There is a prediction that the rise

in fluctuations in the multiplicities and the transverse momentum of produced particles

would be the signature of the critical point [4]. Currently the first measurements of ion-ion

interactions are analyzed, and next runs are planned for the future. For the full plan of

ion program see Figure 1.3

Large statistic of p+p and p+Pb interactions

The data coming from the nucleus-nucleus interactions are usually compared and inter-

preted with respect to the proton-proton and proton-nucleus data. Thus large statistic

of such interaction would be desirable, and by the time they were not systematically

8

Figure 1.2: The phase diagram of the strongly interacting matter [3]. (a) The currentlyavailable world data. (b) The planned scan of the phase diagram by the NA61/SHINEexperiment. Scan is done with the different system size and energy.

Figure 1.3: The scheme of the planned ion program of NA61/SHINE experiment.

measured. The additional advantage of data recorded by NA61/SHINE is that all the

interactions, together with nucleus-nusleus measured by NA49 exeriment, are recorded by

the same detector. The NA61/SHINE experiment intends to collect massive data set on

the p+p and p+Pb interactions at 158 GeV/c. The analysis of records, which will be

collected, will be focused on the particles with high transverse momentum (pT ). This data

are also needed in the iinterpretation of the measurements of Pb+Pb interactions made

by NA49 experiment.

Reference data for neutrino and cosmic-ray experiments

The additional goal of the experiment is to collect the reference data for the neutrino and

cosmic ray experiments. Na61/SHINE experiment in the collaboration with T2K (Tokai-

to-Kamioka) experiment have measured the products of proton-carbon interactions on the

energy 31 GeV, whichc is the same reaction as this leading to production of neutrino beam.

The measurements enabled a better estimation of the neutrino flux by the analysis of the

hadron production, from which decays the nutrinos are produced. The measurements were

performed on a thin (2 cm) carbon target, and also on the exact replica (1 m) of the target

9

used in the J-Parc laboratory, where neutrinos for T2K experiment are produced. The

measurements of pions and positive kaons yields were already partially analyzed and pub-

lished [5, 6, 7], and used in the T2K analysis leading to the determination of the neutrino

flux [8].

Moreover the data from the hadronic collisions are also useful as the reference for the

cosmic ray experiments [9]. The theoretical models, used in the analysis of the data, have

unphysical discontinuities in predictions. Additionally to the proton-proton and nuclear

collisions, there were also two dedicated runs, with pions (π−) from secondary beam

interacting on the carbon target with energies of 158 and 350 GeV. This setup mimics

well the interaction in air showers: pions colliding with nitrogen and oxygen atoms due to

the similar atomic mass (A) as carbon (equal to 14, 16, and 12 respectively).

1.1.2. NA61 Detector

The detector of NA61/SHINE experiment is the upgraded NA49 detector [10]. Its outline

is presented in Figure 1.4. As can be seen, the most upstream part of detector is a set of

beam detectors, which checks the quality and the composition of a beam, as well as plays

the role of triggers. This consists of:

CEDAR (Cherenkov Differential counter with Achromatic Ring Focus; C1) and

Cherenkov threshold counter (C2): used for the beam particle identification and

for the analysis;

a set of scintillator counters: there are 3 veto counters (V0, V1, V2) - with a hole

at the beam axis to neglect particles divergent form the beam, as well as 4 counters

at the beam axis: both for the beam triggering (before the target: S1, S2) and the

interaction triggering (after the target: S4, S5);

BPD (Beam Position Detector: BPD-1, BPD-2, BPD-3): consisting of three propor-

tional chambers, used for determining the position of the beam, then extrapolated

to the point of interaction with the target.

The target can be liquid (hydrogen target) or solid (carbon, beryllium target), and 10%

of the data is collected with target removed. The data collected without the target are

important in analysis to take into account the non-target interaction verticles in detector

material. Next there is a set of Time Projector Chamber (TPC) detectors: two vertex

TPCs (VTPC1, VTPC2) inside the magnetic field of two dipole magnets, with a small

gap TPC (GTPC) between them and two main TPCs (MTPC-L, MTPC-R). The setup

of TPCs as well as the principle of their work is described in the next section. Behind the

MTPCs there are three Time-of-Flight (TOF-L, TOF-R, TOF-F) scintillator detectors.

The most downstream part of the detector is the Projectile Spectator Detector (PSD) used

10

Figure 1.4: The outline of the NA61/SHINE detector setup.

in ion programme: a calorimeter created with scintillator and lead layers. The calorimeter

is used to count the number of non-interacting nucleons in the beam particle.

Time Projection Chambers

The Time Projector Chamber (TPC) is the detector measuring the three-dimensional

tracks of many particles at the same time. The Time Projection Chamber may be viewed

as the combination of a multi-wire proportional chamber (MWPC) with a drift chamber.

The scheme in Figure 1.5 presents the principle of the operation of the detector. Due to

the electric field in the volume of detector, the electrons, created by ionization caused by

the passage of a charged particle, are transported to the readout pads. Then, when the

detector is active, they pass through the gating grid wires, which have electric field set as

in environment, and come to the MWPC-like part of the detector. The closed gating grid

avoids the undesired multiplication of electrons in time between measured events. Close to

the sense wires the electric field is much higher than the average in the whole volume. It

causes the acceleration of the electrons and their multiplication due to the collisions with

gas. In the same time the ions are created and they drift into the opposite direction than

the electrons. The electrons are then collected by the sense wires, and the excess of ions

causes a change in the electric field, which is registered on the readout pads. Thus, from

the information on the position of an activated readout pad the position of particle track

in two dimensions is obtained. Information about the third dimension is obtained from the

time of drift in the detector volume. Thus the calibration and precise determination of the

drift velocity are essential. Additionally, the amplitude of the signal is measured, which

then is used in analysis leading to identify the mass of the particle by the characteristic

energy loss (dEdx ). The set of information: the position and amplitude of signal is called a

cluster. It is important to note, that due to the gaseous, sparse interior of the detector

the production of particles in secondary vertices is kept at a low level, thus limiting the

contamination of the particles from the interaction vertex.

11

In the NA61/SHINE experimental setup there are five TPCs of total volume about

Figure 1.5: The scheme of Time Projection Chamber detector and the detection procedure[9].

40 m2. Two front TPCs with dimensions 2m Ö2.5m Ö1m are located inside the magnet

coils; in their volume there is a magnetic field of maximally 1.5T and 1.1T (for VTPC-1

and VTPC-2 respectively) parallel to the electric field. This setup reduces the distortion of

the electron drift to the readout. The magnetic field bends the trajectories of the charged

particles depending on their momenta, thus introducing a tool for its determination. VT-

PCs have a gap along the beam line to reduce interference from the noninteracting beam

particles, e.g. ions causing massive ionization in the TPCs. There is GTPC between

VTPCs and it enables to track the particles with small production angle. Down the

beamline, after the VTPCs and GTPC, there are two MTPCs (R and L for right and left)

of dimension 3.9m Ö3.9m Ö1.8m. The tracks in the MTPCs are straight due to the lack

of magnetic field, but the detectors are optimized to precisely measure the energy loss.

Combined with the information on the momentum from the track curvature it enables the

identification of a particle.

The important feature of the TPCs is the choice of a gas mixture as it has effects

on every step of the detection process: the ionization, the electron drift and the gas

amplification. Thus the gas mixture should be chosen in such a way that it will:

maximize the ionization and the gas amplification to maximize the sensitivity of the

detector,

have a output signal proportional to the primary charge to enable dEdx analysis,

have a high drift velocity to enable the full readout of the cluster in the time between

12

subsequent events,

keep a low diffusion rate of electrons to maximize the spatial resolution,

have a low photons production rate during electron drift to avoid secondary electron

avalanches.

To optimize the fulfillment of, sometimes contradictory, requirements above a set of tests

needed to be done [11]. This resulted in the following composition of a gas mixture:

VTPC and GTPC: 90% Ar and 10% CO2,

MTPC: 95% Ar and 5% CO2.

The addition of the so-called quenching gas, here CO2, reduces the diffusion rate of elec-

trons, but at the same time it also decreases the drift velocity, thus its content needs to

be balanced. The level of oxygen and water impurity in TPCs needs to be controlled and

minimized, as they cause the loss in the drifting charge.

1.1.3. Reconstruction of Events

The outcome of the detection procedure is raw data, which needs to be then postprocessed

to obtain the final format which then may be analyzed. The reconstruction is based

on the external parameters and the detector characteristics, determined by calibration

procedure. The main effort lies in the track reconstruction and particle identification.

The reconstruction of events is done by reconstructing the tracks of particles in TPCs.

This enables the determination of momentum of particles. The identification of particles

is done using just the information on energy loss in TPCs, or also with the additional

information from TOFs.

Track reconstruction

The track reconstruction is based on 4 steps:

finding the clusters: the position and amplitude of a signal,

reconstructing the track segments in each TPC separately,

reconstructing global tracks from all TPCs and fitting them to the interaction point,

determining the momentum from the fitted tracks curvature.

The particle traversing the detector ionizes the gas and leaves clusters along its track.

The procedure, taking into account the magnetic field in the TPC, combines the clusters

into the track, and then tracks from all TPCs are combined into global tracks. The tracks

may start in the main vertex, but there are also well-defined tracks from the neutral par-

ticles produced in the vertex, so called V0-tracks, which are then appearing in TPC after

13

the neutral particle’s decay. The secondary particles produced in the detector material, or

coming from unknown sources decrease the efficiency of the reconstruction procedure. The

direction of the readout pads is optimized to the ”right-side track” (RST): the particles,

whose tracks are on the same side of the detector as the side on which it was produced,

and thus the ”wrong-side tracks” (WST) from the particles, whose tracks were bend on

the other side of the detector than the side on which it was produced are removed from the

analysis. Then to the reconstructed track the momentum, from the bending of the track,

is assigned. Figure 1.6 shows the reconstructed tracks from the p-C interaction (NA61)

and Pb-Pb interaction (NA49). It is clearly visible that multiplicity of particles increases

with the growth of the mass number of the interacting nuclei.

Figure 1.6: The tracks reconstructed in the NA61/SHINE and NA49 detectors: (a) thep+C interaction at 31 GeV/c; (b) the Pb+Pb interaction at 158 GeV/c [3].

Particle identification

The particle identification is based on the energy loss measurement in the TPC volume (dEdx ), in case of intermediate momentum of particles supported by information from Time-

of-Flight detectors (ToF).

The dEdx identification is based on the Bethe-Bloch formula:

−〈dEdx〉 = Kz2Z

A

1

β2·[ln

(2mec

2β2TmaxI2(1− β2)

)− β2 − δ(βγ)

2

](1.1)

where c is the speed of light, �0 the vacuum permittivity, β = v/c, me the electron charge

and rest mass respectively, n electron density, z is the charge of the particle travelling

through the material in units of electron charg, A and Z are atmic mass and number of

absorber, Tmax is a maximum kinetic energy that can be imparted to a free electron in a

single collision, K is a constant and δ(βγ) is the density-effect correction. The measure-

ments of the energy-loss are based on the measure of charge of clusters on the track of

the particle. The plot of energy loss (〈dEdx 〉) versus the particle momentum leads to the

14

separation of different particles (see Figure 1.7), as the Bethe-Bloch formula depends on

the velocity (β). The Bethe-Bloch formula, however, is not monotonic, thus the plots are

crossing. As could be noticed, due to the crossing of a plots, the dEdx is reliable in the

relativistic region (over few GeV/c) and for the low momentum region.

Figure 1.7: The plots of energy loss with respect to the particle’s momentum for positive(a) and negative (b) particles. The data intersects in the middle momentum region [3].

In the region which is problematic for the dEdx identifications the combined energy

loss and Time-of-Flight procedure is used. The Time-of-Flight (ToF) detector, combined

with the track reconstruction allows determining the mass of the particle according to the

equation

m2 = p2(c2t2TOFl2

− 1), (1.2)

where p is particle momentum, tTOF is time of flight from the interaction point to the ToF

detector and l is length of the trajectory of particle. Figure 1.8(a) presents the plot of

reconstructed squared mass with respect to the momentum of the particle, which is well

separated in low and middle momentum range. Figure 1.8(b) also presents the identifi-

cation through the information obtained from energy loss and ToF. As can be seen the

signals of different particles are well separated, and combined dEdx -ToF method is most

desired in the middle momentum range.

1.2. Nuclear-Scattering Models for Monte Carlo Simulations

1.2.1. Monte Carlo simulations in Particle Physics

The Monte Carlo (MC) simulations play a key role in every stage of a particle physics

experiment:

15

Figure 1.8: (a) The graph of the reconstructed squared mass with respect to the momentumobtained with ToF detector. (b) The 2D graph of particle identification obtained fromcombined information from ToF detector and energy loss for middle momentum region[3].

during the planning of the detector: enabling simulation of its performance

supporting the calibration

during data-analysis used to correct the measurements for the detector and known

physical effects

used for comparison between experimental data and the theory.

One can distinguish two main steps in the particle physics MC simulations: simulating

passage of particles through detector and generating particles in an interaction. The

first type of simulation needs the precise description of geometry of the detector, as the

behavior of the particle depends on the material in which it travels. In every step of

the simulation, based on the random-number generator, the interaction of particle with

detector is determined. All secondary particles produced during this step need also to be

followed in the simulations making the task very computationally demanding. The latter

branch of MC simulations is governed by the Standard Model for partonic (hard QCD)

or electroweak interactions or by hadronic models for so-called soft QCD processes. As

the processes on the hadronic level, such as nucleus-nucleus or nucleon-nucleon collisions,

cannot be described by the perturbative quantum chromodynamics (QCD), there is a

need to use hadronic models based on semi-empirical theories. They will be described in

more details in the next section. In an experiment such as NA61/SHINE the choice of

proper hadronic model is essential, as the obtained data are outside of regime described

by perturbative QCD. Additionally the processes investigated by the experiment, such as

the phase transition or existence of QGP, may not give evident signals and a quantitative

analysis needs to be done. Monte Carlo simulations may be useful in such a situation on

two ways: supporting the precise data-analysis and giving the reference for the different

scenarios of the state of matter after collision.

16

1.2.2. Nuclear Scattering Models: EPOS and VENUS

The hadronic models VENUS [12, 13] and EPOS [14] are based on the Gribov-Regge theory

(GRT). This theory was a basis for various models, which proved to be in good agree-

ment with the experimental data. As this theory is appropriate for the interaction with

relatively low particles density, it needs an extension for the high-energy and heavy-nuclei

collisions. In such situation there is a need to include so-called rescattering: procedure in

which the produced hadrons scatter again, as the energy density in such collisions is high.

After the initial interaction the avalanche of secondary interactions may occur leading to

the thermal equilibrium.

The hadron-hadron interaction is described by the parton model having two contribu-

tions: the parton distribution of a hadron and the elementary parton-parton cross-section

obtained with perturbative QCD. Partons are the elementary constituents of the hadrons

carrying the fraction of total hadron’s momentum. For the high-parton density, which

is the case in the proton-nucleus and nucleus-nucleus collisions, the interaction is treated

by the pomeron-pomeron interactions, where pomerons are the so-called parton ladders

showed in Figure 1.9. This parton ladder contribution needs to be augmented by the de-

scription of the remnants of the hadron (diquarks or antiquarks), which may be viewed as

the ”spectators” of the interaction. The interaction is described by the multiple scattering

in which open parton ladders are present, representing the inelastic scattering, as well

as closed ones, for the elastic scattering, both showed in Figure 1.9. In the next step of

procedure of the scattering, the momentum fractions and the transverse momentum are

assigned for the ends of the ladders. With this information may be calculated the partial

cross-section as a function of the impact parameter b: the perpendicular distance between

the path of a projectile and a target. The partial cross-section is the basis for the Monte

Carlo algorithm.

Figure 1.9: (a) The Feynman diagram presenting the creation of parton ladder in interac-tion of two nuclei and a schematic graph; (b) open and closed parton ladders correspondingto the inelastic and elastic scattering respectively [14].

17

To retrieve the information about the hadrons produced in the interaction there is a

need to construct the strings from the free parton lines of pomerons. The classical string

approach, with the string being the two-dimensional surface in four-dimensional spacetime

and with the transformations governed by the gauge group representation is a basis of the

description of the strong interactions of GRT. It can be viewed that the string’s endpoints

represent the quarks and the string interior represents the gluons. An important feature

of the procedure is the algorithm for the string fragmentation: that is the description of

the evolution of the system and the prescript for final hadron’s production. Figure 1.10

represents the string fragmentation and the continuation in the future of two new strings.

The string fragmentation is governed by random-number generators. The fragmentation

model used in the VENUS and EPOS is based on the AMOR (Artru-Mennessier Off-

shell Resonance) model, which determines the point in which fragmentation takes place

to maintain all the required properties such as locality and covariance. In the used model

the fragmentation does not occur on the mass shell, which means that the masses of frag-

mented strings do not refer to the masses of the hadrons but they need to be greater than

minimal mass of the hadron constituted from the given quark. The fragmentation then

continues until the final strings have masses below cutoff, and then they are identified with

the resonances. During every fragmentation also the transverse momentum is assigned.

Additionally, to obtain the heavy quark final states, during fragmentation there is a set of

probabilities to create a heavy quark-antiquark pair.

Figure 1.10: The scheme of string fragmentation leading to production of two new strings:graph presents the propagation of a string, which breaks (line segment AC) into two newstrings continuing the propagation to the future. The lines correspond to the endpointsof the string, which correspond to the quark or antiquark [13].

To conclude, both models, VENUS and EPOS, belong to the group of models based on

18

the Gribov-Regge theory of partons and phenomenological model of the string fragmen-

tation. They are both well suited and designed to take into account high-density effects

such as the formation of the quark-gluon plasma, which is hypothetically possible final

state of the nucleus-nucleus high energy collisions. EPOS model have been developed

from VENUS model, which is sometimes referred as the old generation model [15]. Thus,

EPOS model, which is still developed and updated [16], may be viewed as the successor

of VENUS model.

19

Chapter 2

Analysis

The analysis leading to tuning of particles spectra and the so-called h− correction in h−

analysis were based on the Monte-Carlo productions used by the NA61/SHINE experi-

ment. The h− analysis retrieves the spectra of negatively charged pions from the spectra

of all negative particles. The MC productions were generated with the hadron models

VENUS and EPOS. The particles were propagated through the detector with use of the

GEANT3.2.1 package. The postprocessing was the same as with the experimental data.

The records from the particles from the simulated p+p interaction together with their

following strong and electromagnetic decays will be referred as the ”generated”, and these

data after the reconstruction procedure will be referred as the ”reconstructed”. The anal-

ysis was done using series of programs, written with use of ROOT61 package in C++

programming language.

In the first step of the project the total multiplicities of strange particles: Λ , Λ̄, K0s ,

K− and K+ as well as the negatively charged pions were analyzed as a function of the

interaction energy. The information obtained with the Monte Carlo models were com-

pared with the available reference data from the literature [17, 18] and the preliminary

NA61/SHINE measurements [19, 20]. The results were then used in the next steps of the

work to tune to the spectra obtained from MC models.

Next step of comparison between measured and simulated records was based on a con-

struction of the transverse mass spectra, where transverse mass is defined by the equation:

mT =√m2 + p2T , (2.1)

where m is particle’s mass and pT is the transverse momentum, without any constrains

21

on rapidity. Rapidity is the kinematic variable, which may be defined as:

y =1

2ln

(E + pzE − pz

)=

1

2ln

(E + pzmT

), (2.2)

where pz is longitudinal momentum and E is energy. Important note is that the rapidity

is different for particles with the same momentum but different mass. Then to the spectra

an exponential function was fitted:

1

mT

dn

dmT= AT · e−

mTT . (2.3)

The inverse slope parameters T were then plotted with respect to the energy of the proton

beam and compared with the experimental reference data [21, 22].

The second task of the project was the construction of corrections to the rapidity-

transverse momentum spectra of particles important in h− analysis obtained from MC

simulations. The corrections to the MC spectra constructed with use of reference experi-

mental data will be called the adjustments to avoid confusion with h− correction described

in last part of analysis. The h− analysis is based on the theoretical and experimental ob-

servations that the vast majority of negatively charged particles are π− with admixture

of electrons, negative kaons, antiprotons, etc. Actually electrons may be eliminated in

the early stage of analysis due to the good separation in energy loss analysis (see Figure

1.7). Thus when in the thesis the expression negatively charged particles is used it refferes

to negatively charged particles except electrons. The h− analysis enables, after series of

corrections, to obtain the pions spectra without the need for direct identification. The

particles which were the subject of the adjustments are the negatively charged particles:

K− and p̄ and secondary pions produced in decays of neutral particles: K0s and Λ. The

proposed adjustments were based on the comparison done in the first part of the project

and preliminary results of NA61/SHINE experiment. The adjustment was applied as the

multiplicative correction cN to the MC reconstructed spectra:

nMC,adjustedN (y, pT , E) = cN (y, pT , E) · nMC,reconstructedN (y, pT , E), (2.4)

where y is rapidity, pT transverse momentum and E the energy of p+p interaction. Thus

the adjustments may be viewed as the spectra in rapidity and transverse momentum which

are multiplying the reconstructed MC spectra bin by bin to tune them to the experimental

data. The adjustments and spectra of particles are presented as 2D spectra with bin’s size

0.2 in rapidity and increasingly from 50 to 250 MeV/c in transverse momentum, as can be

seen in Figures in Sections 3.3. The particle spectra were tuned in three ways, depending

on the available data, and are presented below:

for π−: Every bin of spectra was rescaled by the divided preliminary spectra mea-

22

sured by NA61/SHINE experiment [19] and spectra generated from MC models and

additionally whole spectra were scaled by the total pion multiplicities:

cπ−(y, pT , E) =〈π−〉refdata〈π−〉NA61

· nNA61(y, pT , E)nMC,generated(y, pT , E)

, (2.5)

where 〈π−〉 are the total multiplicities and n(y, pT , E) are the spectra bins.

for secondary π− from Λ and Ks0 decays: the spectra were scaled by a constant factor

constructed from total multiplicities:

cΛ/K0s (E) =〈Λ/K0s 〉refdata(E)〈Λ/K0s 〉MC,gen(E)

, (2.6)

where 〈Λ/K0s 〉 are the total multiplicities.

for p̄ and K−: the adjustment was based on the divided preliminary NA61/SHINE

spectra [20] and spectra generated from MC models for interaction energy 158 GeV,

to which was fitted the bi-linear function:

fp̄/K−(y, pT ) = A · y +B · pT + C. (2.7)

The first step of analysis showed that the discrepancies between data from MC model

and experiment increase with the energy, thus for lower interaction energies the fitted

function was scaled down linearly:

Sp̄/K−(E) = 1 +E − 20

158− 20. (2.8)

In the result the correction is defined as:

cp̄/K−(y, pT , E) = 1 +E − 20

158− 20· (A · y +B · pT + C − 1) (2.9)

Last part of the project was a construction of the h− corrections, which is needed in

h− analysis to correct the spectra of negatively charged particles (marked h−) for parti-

cles different than primary pions (π−(V 0)). The particles contributing to the correction

are other negative particles (µ−, K− , p̄), secondary pions from decays of neutral parti-

cles called feed-down (π−(Λ), π−(K0s )) and other negative particles, mostly pions from

secondary interaction vertices (marked as others):

h− = π−(V 0) +K− + p̄+ π(K0s ) + π(Λ) + µ− + others. (2.10)

The feed-down are the secondary pions which were falsely fitted to the primary vertex, and

thus their reconstructed momentum is different than the real momentum. Additionally,

the momentum of secondary pions is weakly correlated with the momentum of particles

from which they were produced.

23

The correction is done with use of spectra generated from MC models and then recon-

structed. The three ways of applying the corrections were proposed, which in the ideal

situation, when the MC models describe exactly the experimental data, should be the

same.

h− additive correction: the contribution from particles other than primary pions was

subtracted from the spectra

[π−]add = [h−]NA61 − ([h−]− [π−(V 0)])MC,rec (2.11)

h− multiplicative correction: the spectra were scaled by the fraction of primary pions

in all negative particles

[π−]mul = [h−]NA61 ·[π−(V 0)]MC,rec

[h−]MC,rec(2.12)

h− mixed correction: the contribution from the secondary pions and other interfering

particles was subtracted and then it was scaled by fraction of primary pions to sum

of primary negative particles

[π−]mix =([h−]NA61 − ([π−(Λ)] + [π−(Ks0)] + [others])MC,rec)·

·[π−(V 0)]MC,rec

([π−(V 0)] + [K−] + [p̄] + [µ−])MC,rec,

(2.13)

where [h−]NA61 stands for spectra of negatively charged partciles except electrons mea-

sured by NA61/SHINE experiment and [x]MC,rec for spectra of particle x (as listed above)

generated and reconstructed from Monte Carlo model. The corrections were also improved

by the adjustments to the particles constructed in previous step of project. The methods

of application of the h− correction were compared to find the most suitable one. The

corrections enabled also the assessment of the adjustments.

24

Chapter 3

Results and Discussion

The results of the comparison of the Monte-Carlo models and experimental data are

presented on the series of plots. Also the adjustments to the particles responsible for the

h− correction and the corrections itself are presented in the form of the 2D histograms

for the better overview. The analysis was done for all the available interaction energies,

but in thesis are presented only the spectra for the extreme interaction energies: 20 and

158 GeV. In the next sections the results will be discussed and related to the existing

literature data and preliminary measurements of NA61/SHINE experiment.

3.1. Multiplicities of Particles

Figure 3.1 presents the total multiplicities of the particles from the proton-proton collisions

generated from the Monte Carlo models: VENUS and EPOS and reference experimental

data [17, 18]. The data was parameterized with the logarithmic or polynomial function.

The five beam energies from MC simulations (20, 31, 40, 80, 158 GeV) correspond to the

energies used in the NA61/SHINE experiment.

What needs to be noted is that pion multiplicity is plotted against Fermi’s energy:

F [GeV12 ] =

(√s− 2mp)

34

(√s)

14

(3.1)

where√s is center of mass interaction energy and mp is proton mass. The 〈π−〉 multiplic-

ity increases linearly with F in p+p interaction [23]. This linear fit to 〈π−〉 was used toconstruct the ratio of strange particle’s multiplicities to the pion’s multiplicity presented in

Figure 3.2. For better comparison the MC multiplicities divided by the experimental data

fits are plotted in Figure 3.3. Additionally, the graphs with strange particle multiplicities

divided by the multiplicities of negative pions are presented in Figure 3.2. These graphs

are presented to demonstrate the contribution of the particles in h− analysis. Finally, in

Table 3.1 are collected the particle’s multiplicities from the MC data and functions fitted

25

Figure 3.1: The total multiplicities of particles with respect to the interaction energy. Theliterature data were parametrised by polynomial or logarythmic function.

to the reference data of Figure 3.1.

It is visible in Figure 3.1 that the total multiplicity of EPOS model agrees better

with the experimental reference data. It is consistent with the fact, that it is a later

model, which was revised with respect to VENUS. From Figures 3.1 and 3.2 it can be

also noticed that both models usually overestimate the multiplicities of the particles. The

negative pions multiplicities are well described by both models, as can be seen in Figures

3.1 and 3.3. The discrepancies are lower than 10%. In case of Λ baryon it is clearly visible

that the overestimation is growing with the decrease of the interaction energy and yields

over factor 2 for VENUS and 1.5 for EPOS for the lowest energy: 20 GeV. From the

26

graph of the relative multiplicities it is visible, that Λ is produced on the level of 10% of

pion production. It is important, as the branching ratio of lambda’s decaying in negative

pion is on the level of 60%, and thus have significant contribution in feed-down correction,

especially at low energies, where the yields of other interfering particles are low, but also

the discrepancies between the experimental data and MC models are the largest.

Figure 3.2: The ratio of total multiplicities of strange particles to negative pions withplotted versus the interaction energy.

The antilambda baryons are much more rarely produced, on the level lower than 1%.

They are described better than lambdas by the MC simulations. The VENUS data are

slightly overestimated, but also the experimental values have large uncertainties. In the

case of positive kaons main discrepancies between experimental data and MC models are

visible in low-energy region, and they are decreasing for the higher energies. In both cases

of charged kaons EPOS model performs slightly better than VENUS. Especially in the

27

Figure 3.3: The total multiplicities of particles generated from MC models divided by theparameterization of experimental data, plotted with respect to the interaction energy.

case of positive kaons, the EPOS model is in good agreement with experimental data with

discrepancies lower than 10%. Negative kaons are more important for h− analysis, as

they, as negatively charged particles, need to be included in the correction to obtain the

negative pions spectra. Although that in Figure 3.3 it seems that the discrepancies are

the biggest in the low energy region, but in Figure 3.1 it is visible, that the absolute error

is larger for the two highest energies. The additional problem is the lack of experimental

points in the region of 158 GeV for charged kaons: the neighboring experimental records

are from the energy around 70 GeV and 500 GeV. The neutral short-living kaons, similarly

as Λ baryons contribute to the h− analysis via the secondary π−, with branching ratio on

their production equal to around 70%. Both models overestimate the multiplicities of K0s ,

with better performance of EPOS.

28

Energy 〈π−〉 [ref] 〈π−〉 [NA61] 〈π−〉 [EPOS] 〈π−〉 [VENUS]158 2.393 2.424 2.404 2.31180 1.866 1.927 1.989 1.76040 1.398 1.497 1.569 1.34031 1.242 1.333 1.412 1.21920 0.988 1.066 1.146 1.010

Energy [GeV] 〈Λ〉 [ref] 〈Λ〉 [EPOS] 〈Λ〉 [VENUS]158 0.110 0.116 0.12580 0.109 0.108 0.14340 0.080 0.099 0.13931 0.072 0.094 0.13720 0.061 0.093 0.133

Energy [GeV] 〈K0s 〉 [ref] 〈K0s 〉 [EPOS] 〈K0s 〉 [VENUS]158 0.160 0.183 0.16680 0.116 0.138 0.15540 0.071 0.096 0.11631 0.059 0.080 0.10320 0.044 0.054 0.085

Energy [GeV] 〈K+〉 [ref] 〈K+〉 [EPOS] 〈K+〉 [VENUS]158 0.282 0.243 0.27780 0.219 0.195 0.22640 0.155 0.146 0.18331 0.131 0.128 0.17120 0.091 0.098 0.148

Energy [GeV] 〈K−〉 [ref] 〈K−〉 [EPOS] 〈K−〉 [VENUS]158 0.180 0.141 0.14880 0.125 0.099 0.10240 0.070 0.060 0.06431 0.049 0.046 0.05420 0.014 0.025 0.036

Energy [GeV] 〈Λ̄〉 [ref] 〈Λ̄〉 [EPOS] 〈Λ̄〉 [VENUS]158 0.019 0.011 0.01680 0.005 0.006 0.01140 0.002 0.002 0.00431 0.001 0.001 0.00220 0.001 0.001 0.002

Table 3.1: The total multiplicities of particles from MC models parameterized referencedata and for pions from preliminary NA61/SHINE experiment.

Table 3.1 collects the total multiplicities obtained during analysis. The reference data

comes from the parameterization of the reference data from literature. For negative pions

are also included the preliminary multiplicity obtained with NA61/SHINE experiment. It

agrees well with other experimental data on the level of few percent.

29

3.2. Transverse Mass and T Parameter

Next part of the project was based on the transverse mass analysis of events generated

with MC models and comparison of the obtained inverse slope parameter (T ) with the

experimental data. The Figure 3.4 presents the spectra in transverse mass ( 1mT ·dndmT

).

The spectra were derived without any constraints on the rapidity or production angle.

Exponential function (2.2) was fitted to the points. The exponential function is in good

agreement, especially for the kaons and for hyperons for low mT region, what is consistent

with experimental records: the experimental data were available up to 0.6 GeV [22]. In

case of hyperons, the agreement holds in range 0-0.4 GeV, which is in accordance with

experimental data [21]. The exponential function fitted to the MC spectra describes well

the same region as the available experimental data, thus enables the comparison of T pa-

rameter of full spectra. On the other hand, the logarythmic scale shades that the absolute

errors of fit in the region of high 1mTdndmT

.

In Figure 3.5 the T parameter versus the interaction energy was plotted for both MC

models and in the last row also from experimental records. The solid, straight line on the

plots is the fit to the experimental data taken from the references [21, 22]. According to

the authors, the dependence of inverse slope parameter T on the collision energy should

be linear. It is important to note, that the fit was made for the wide range of interaction

energy, up to nearly 2 TeV. In the range of interest (30-160 GeV), however, there are few

data-points and they usually have large errors. Since the errors are bigger as the discrep-

ancies between the models, the analysis may not be conclusive.

The discrepancies are the most significant in case of Λ hyperons. The linear fit to

the experimental data lays between these two models, but VENUS datapoints are closer

to it. In case of the Λ̄ baryons the discrepancies between MC models also are significant,

but unfortuantelly the experimental records are lacking. In case of kaons all points of MC

models lay below the experimental linear fit. In case of data from MC models for the

neutral and positive kaons the points have similar values with VENUS points having more

flat dependence on the beam momentum than EPOS, and crossing around 60 GeV/c. For

the negative kaons the EPOS points increase faster with the interaction momentum, and

are always lying above VENUS points, and are thus closer to the experimental fit.

30

EPOS VENUS

Λ :

Λ̄ :

K0s :

K− :

K+ :

Figure 3.4: The spectra of transverse mass obtained with MC models with the fittedexponential functions.

31

Figure 3.5: The inverse slope parameter T versus the interaction energy. Solid line rep-resents the parameterization from the experimental records. In last row are presentedexperimental records with fits from [21, 22]

32

3.3. Tuning of the Particle Spectra from Monte Carlo simu-

lations

In Figure 3.6 there are presented the negative pion spectra and spectra relative to the

all negatively charged particles. As can be noticed from plots the spectra produced from

both models are in good agreement, what is in agreement with Figure 3.1, showing good

agreement of models in case of total multiplicities. With the increase of interaction energy

the total multiplicity grows and the rapidity range is wider, especially in the low transverse

momentum region. Negative pions’ contribution to all negative particles is on the level of

90% for interaction energy 20GeV, and it increases for higher energy. The relative spec-

trum of EPOS model is slightly higher than this of VENUS model. The regions in which

contribution of particles other than pions is important is especially the low transverse

momentum region for low interaction energies and high transverse momentum region for

high interaction energies.

Figure 3.7 shows the adjustment of the pion spectrum as described in Analysis section

(see eq. (2.5)). The adjustment is the highest for the interaction energy 20GeV. In general,

the tendency is that the number of pions from MC simulations needs to be increased in

high pT region, and decreased in low pt and high y region. The adjustment is decreasing

with the interaction energy in case of EPOS models, but in case of VENUS model the

adjustment is smallest for the intermediate interaction energies.

In the h− analysis the important step is to take into account the fact that the recon-

structed primary particles can originate from the secondary pions produced in the decays

of the neutral particles: hyperons Λ or neutral kaons K0s . The adjustment of the spectra

reconstructed from MC models was a constantfactor according to the total multiplicities,

presented in Table 3.2. Figure 3.8 presents spectra of lambda baryons and their relative

contribution to all negatively charged particles. As one can notice the highest yield of the

secondary pions is for the low energies, with the maximum at low transverse momenta.

This indicates that the inclusion of the feed-down is the most important at the energies

where the discrepancies between the models and experiment are the largest.

In Figure 3.9 there are presented the spectra of pions produced from the decays of

neutral kaons which were produced and reconstructed from MC models. The adjustment

was constructed in the same way in the case of lambda hyperons, by rescaling of the whole

spectra by the ratio of total multiplicities (see Table 3.2). The spectra obtained with both

models are in quite good agreement, VENUS spectra are slightly wider in rapidity than

EPOS. The secondary pions from neutral kaons decay, similarly as from lambda decays,

33

EPOS:

VENUS:

Figure 3.6: The reconstructed spectra of primary negative pions obtained with MonteCarlo models for interaction energy 20 and 158 GeV (left figures) and the correspondingratios of primary π− to all negative particles presented in percent (right figures).

contribute to negatively charged particles spectra mainly in low transverse momentum

spectra. The difference is that the yield of π−(K0s ) grows with the interaction energy,

opposite to the lambda’s case.

Other particles contributing to the h− correction are primary negative hadrons which

34

EPOS:

VENUS:

Figure 3.7: The adjustment of the negative pions obtained using preliminary NA61/SHINEspectra and total multiplicity from the world results compilation.

may be misassigned in h− analysis: the negative kaons and antiprotons. Figures 3.10

and 3.11 present the steps of construction of the bi-linear adjustment, as described in the

Analysis section. The histograms presented in the bottom rows of Figures show how well

the parameterization describes the ratio of the experimental and MC spectra. As can be

seen, in case of antiprotons the ratio between the spectra’s ratio and fitted function is

between 0.8-1.2, thus in satisfactory accordance, and in case of kaons accordance is even

35

Energy [GeV] cΛ [EPOS] cΛ [VENUS]

158 0.948 0.88080 1.009 0.76240 0.808 0.57631 0.766 0.52620 0.656 0.459

Energy [GeV] cK0s [EPOS] cK0s [VENUS]

158 0.874 0.96480 0.840 0.74840 0.740 0.61231 0.738 0.57320 0.815 0.518

Table 3.2: The adjustment factor by which the spectra of secondary pions from neutralparticles decays are scaled.

better (between 0.9-1.2). The adjustment shows that the models underestimate the yield

of particles for high transverse momentum and overestimate for the low transverse mo-

mentum and high rapidity. Table 3.3 collects the values of the parameters of the fitted

function.

A B C

p̄ EPOS -0.124 0.766 0.674p̄ VENUS -0.469 0.290 0.972K− EPOS -0.252 0.281 0.995K− VENUS -0.299 0.710 0.851

Table 3.3: The parameters of the fitted plane from Figures 3.10 and 3.11, as marked inequation (2.7).

The Figures 3.12 and 3.13 present the spectra of antiprotons and negative kaons re-

spectively. The shape of both spectra is similar, but the kaon yield is around three times

larger. The most of the particles are in the region of low transverse momentum and middle

rapidity. The maximum region is shifted from the position y = 0 because of the change of

the rapidity variable: from the rapidity calculated with antiproton or kaon mass to rapid-

ity calculated with the pion mass. In Figures 3.10 and 3.11, where rapidity is calculated

with the corresponding particle mass, the maximum is in the position of low pT and y = 0.

The adjustment was calculated only for the proton beam of energy 158 GeV. Ac-

cordingly to Figure 3.1 the models describe well the experimental data for 20 GeV and

discrepancies grow with the energy, thus linear scaling of the adjustment was proposed as

described in the Analysis section (see eq.(2.8)). The spectra of antiprotons (Figure 3.12)

and negative kaons (Figure 3.13) are presented in coordinates with rapidity calculated with

36

pion mass assumption, and thus the adjustments are asymmetric with respect to y = 0

as can be viewed in Figures 3.14 and 3.15. The tuning reduces the number of particles in

the low pT region and increases it in the high pT region. It can be noted, accordingly to

Figures with relative spectra, that the corrections from secondary pions of neutral parti-

cles and misassigned negative particles are complementary: they are important for other

energies and other regions of spectra.

Figure 3.16 presents of spectra called as ”others”, as defined in Analysis section. They

originate from various sources, mainly from the secondary interaction vertices in the de-

tector material. They originate from various primary particles, thus it is difficult to define

well the adjustment and it was not included in scope of the project. The contribution of

such particles to the spectra of all negative particles is luckily quite low, on the level of

2-5 %, and it is the most important in the low pT -low y region and very high pT region.

37

EPOS:

VENUS:

Figure 3.8: Spectra of secondary pions from lambda decays, reconstructed as primaryparticles obtained with Monte Carlo models for interaction energies 20 and 158 GeV (leftfigures) and the corresponding ratios of π−(Λ) to all negative particles presented in percent(right figures).

38

EPOS:

VENUS:

Figure 3.9: Spectra of secondary pions from neutral kaons decays, reconstructed as primaryparticles obtained with Monte Carlo models for interaction energies 20 and 158 GeV (leftfigures) and the corresponding ratios of π−(K0s ) to all negative particles presented inpercent (right figures).

39

(1) VENUS EPOS Data

(2) Data/VENUS Data/EPOS

(3) fitted function:VENUS EPOS

(4) fitted function/(Data/MC):VENUS EPOS

y is a rapidity obtained with antiproton mass

Figure 3.10: The steps of construction of the antiproton adjustment for interaction energy158 GeV: (1) the generated MC spectra and preliminary NA61/SHINE spectra; (2) theNA61/SHINE spectra divided by MC spectra; (3) the bi-linear function fitted to thedivided spectra from (2); (4) the fitted function from (3) divided by spectra from (2),showing the quality of the fit.

40

(1) VENUS EPOS Data

(2) Data/VENUS Data/EPOS

(3) fitted function:VENUS EPOS

(4) fitted function/(Data/MC):VENUS EPOS

y is a rapidity obtained with kaon mass

Figure 3.11: The steps of construction of the negative kaon adjustment for interactionenergy 158 GeV: (1) the generated MC spectra and preliminary NA61/SHINE spectra forinteraction energy 158 GeV; (2) the NA61/SHINE spectra divided by MC spectra; (3) thebi-linear function fitted to the divided spectra from (2); (4) the fitted function from (3)divided by spectra from (2), showing the quality of the fit.

41

EPOS:

VENUS:

Figure 3.12: Spectra of antiprotons obtained with Monte Carlo models for interactionenergies 20 and 158 GeV (left figures) and the corresponding ratios of p̄ to all negativeparticles presented in percent (right figures). Rapidity was calculated with pion massassumption.

42

EPOS:

VENUS:

Figure 3.13: Spectra of negatively charged kaons obtained with Monte Carlo models forinteraction energies 20 and 158 GeV (left figures) and the corresponding ratios of K− toall negative particles presented in percent (right figures). Rapidity was calculated withpion mass assumption.

43

EPOS:

VENUS:

Figure 3.14: The adjustment to the antiprotons obtained in Figure 3.10 and scaled withthe interaction energy.

EPOS:

VENUS:

Figure 3.15: The adjustment to the negative kaons obtained in Figure 3.10 and scaledwith the interaction energy.

44

EPOS:

VENUS:

Figure 3.16: Spectra of other negative particles obtained with Monte Carlo models forinteraction energies 20 and 158 GeV (left figures) and the corresponding ratios of others toall negative particles (right figures). Rapidity was calculated with pion mass assumption.

45

3.4. The h− Corrections: Methods of Application and Inclu-

sion of Particle Adjustments

To obtain the spectra of negative pions from the spectra of all negative particles, one need

to apply the h− correction, responsible for eliminating from the spectra particles different

than primary negative pions. In the Analysis chapter there were proposed three methods of

application of this correction. The previous sections clearly indicates that EPOS model is

in better agreement with the experimental data, thus in here mainly results for this model

are presented. The mixed correction will be treated as reference, and other corrections

will be presented relative to it. This method was chosen as the best way of application the

h− correction and used in final h− analysis [24]. This was based on the assumption that

the MC model may deform the spectra of the different particle (negative pions and kaons,

antiprotons) in the similar way. Whereas, the feed-down have a different character, as it

represents not a spectra of particles produced in interaction, but the secondary pions from

decays of primary neutral particles and thus it may require different treatment. This is

important to keep in mind that the above reasoning is only the hypothesis, and it cannot

be confirmed by the comparison of corrections showed below. Actually, in ideal case, if

MC models will describe exactly the experiment, all the corrections should be the same.

On the other hand, the comparisons enables to view the size of the discrepancies between

the corrections, which is a very important feature, as it translates directly on the size of

discrepancies in the final spectra constructed with this corrections.

Figure 3.17 present the mixed corrections obtained from EPOS model. As can be

noticed, the correction generally decreases the number of particles, as it is usually below

1. At low energies, the correction is high in the region of low transverse momentum, what

corresponds to the secondary pions produced in the decay of neutral particles. The cor-

rection grows also on the edge of the spectra: at high rapidity region. The correction in

the area of high pT increases with the growth of the interaction energy.

Figure 3.18 presents the comparison of mixed correction with additive and multiplica-

tive correction. The ratio of additive to mixed correction is usually lower than 1, especially

in region of low transverse momentum. The additive correction is slightly bigger in the

region of high pT . The multiplicative correction has in the majority of the spectrum the

same values as the mixed one. The difference is only in low transverse momentum region,

where the ratio is over 1.2; it indicates that the correction decreasing the particle num-

ber in this region is higher for mixed method. This comparison shows that the additive

correction describes the region of low pT more intensively than the others. On the other

hand, it has a smaller correction in the region of high pT , which is described on the similar

level by the other two. Thus, in a way, the mixed correction can be seen as including both

46

Figure 3.17: The mixed h− corrections from EPOS model.

the contributions, while the additive and multiplicative corrections focus only on one of

them. This comparison, however, do not enable the judgment whether this fact makes the

mixed correction better than either of the other two.

Figure 3.19 presents the ratio of correction obtained with EPOS model to the correc-

tion obtained with VENUS model. The discrepancies between the corrections are mainly

located in the region of low and high transverse momenta. The ratio in vast majority of

spectra is over 1, thus indicating that, as correction is usually below 1, the correction is

bigger for the VENUS model.

Figure 3.20 presents the ratio of mixed corrections without and with the particle ad-

justments presented in previous Section. It shows how the spectra change after application

of the adjustments. The ratio at 20 GeV reaches 0.9 for EPOS and 0.6 for VENUS in

low pT region. Additionally, in case of VENUS model, there is a significant contribution

in high rapidity-low pT region: with the factor up to 0.9, for the higher interaction ener-

gies. Concluding, it is visible, that the adjustments have more impact on the correction

constructed from VENUS model. It is consequence of the fact that this model described

worse the experimental data, and adjustments needed to be bigger.

In Figure 3.21 there are presented again the relative spectra of different methods of

application of h− correction, but with the inclusion of the adjustments. The distribution

of the discrepancies is similar as in Figure 3.18, but their values are 50% smaller.

47

Additive/Mixed:

Multiplicative/Mixed:

Figure 3.18: Ratio of the additive and multiplicative to the mixed h− corrections fromEPOS model.

Figure 3.22 presents the comparison of both corrections obtained with both MC models

with adjustments. The main differences are in the region of high rapidity, near the edge of

spectra and for the high transverse momentum. Comparing Figure 3.22, where the ratio

of h− corrections obtained with EPOS and VENUS models with inclusion of adjustment,

with Figure 3.19, without adjustments, it is visible, that the adjustments result in the

48

Figure 3.19: Ratio of the mixed h− corrections from EPOS model to the one from VENUSmodel.

decrease of discrepancies between h− corrections from other models. It suggests that the

adjustments were calculated and applied correctly, and the both models were corrected to

obtain nearly same final result.

49

EPOS:

VENUS:

Figure 3.20: Ratio of h− mixed corrections from MC models without and with adjustment

50

Additive/Mixed:

Multiplicative/Mixed:

Figure 3.21: Ratio of the additive and multiplicative to the mixed h− corrections fromEPOS model with adjustments.

51

Figure 3.22: Ratio of the mixed h− corrections from EPOS and VENUS model withadjustments.

52

Chapter 4

Conclusions and Outlook

In scope of this thesis was presented comparison of the particle multiplicity and spectra

obtained with Monte Carlo models EPOS and VENUS with available experimental data.

The comparison was then used as a basis for a construction of the adjustments to the

spectra of particles important in the h− analysis: primary negatively charged pions (π−),

secondary negatively charged pions from decays of neutral particles (π−(Λ) and π−(K0s ))

and primary negatively charged particles (p̄ and K−). Finally the methods of application

of the h− correction, responsible for eliminating from the all negative particles spectra

the contribution from the particles different than primary pions, were compared to find

the most effective one. The adjustments to the particle spectra were applied to the h−

correction.

The first important conclusion is that the EPOS model in vast majority of compared

records agrees better with experimental data than the VENUS model. Thus the adjust-

ments applied to the spectra obtained with the EPOS model are smaller than in VENUS

case. It suggests that the corrected EPOS model should be preferred in the h− analysis.

The analysis of the spectra of particles contributing to the h− correction showed that

the contributions come mainly:

from the secondary pions produced in the decay of Λ or K0s for low interaction

energies in the low transverse momentum region

from the negative hadrons like antiprotons and kaons for high interaction energies

in the high transverse momentum region.

The study of methods of application of the h− correction showed that the method includ-

ing both contributions is the mixed one: with the correction from the secondary pions

from weak decays applied additively, while the contribution from primary negative parti-

cles is applied multiplicatively. The additional inclusion of the adjustments to the particle

53

spectra changes the h− correction by up to 20 %.

The h− correction and its adjustments obtained with use of the Monte Carlo models

is just one step in obtaining the final negative pion spectra obtained in the h− analysis

of NA61/SHINE experiment. The comparison of models was also the suggestion for the

choice of the model for the ongoing and future analysis. The description of the other steps

of h− analysis is provided more extensively elsewhere [24] and is connected with the MC

corrections on the reconstruction procedure and its efficiency.

54

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56

Acknowledgments

I would like to thank my supervisor, prof. Wojciech Dominik, for given me opportunities

and support.

My sincere thanks are in order to Antoni Aduszkiewicz, my daily supervisor, for the

support during the realization of the project and writing this thesis. Thank you for your

time, patience and useful advice.

Also I would like to thank all the people from the Particle Physics Group at the Uni-

versity of Warsaw and NA61/SHINE Collaboration for the welcoming me into their group,

friendly work environment and useful remarks on my research. It was a pleasure to work

with you.

Finally, warm thanks to all my close ones for motivating and supporting me.

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