Charged Particle Multiplicity Distributions Research Articles

Charged particle production in pp collisions at s = 8, 7 and 2.76 TeV at the LHC-a case study

We analyze the charged-particle multiplicity distributions measured by the ALICE experiment, over a wide pseudorapidity range, for [Formula: see text] collisions at [Formula: see text], 7 and 2.76 TeV at the LHC. The analysis offers an understanding of particle production in high energy collisions in the purview of a new distribution, the shifted Gompertz distribution. Data are compared with the distribution and moments of the distributions are calculated. A modified version of the distribution is also proposed and used to improve the description of the data consisting of two different event classes: the inelastic and the nonsingle diffractive and their subsets in different windows of pseudorapidity, [Formula: see text]. The distribution used to analyze the data has a wide range of applicability to processes in different fields and complements the analysis done by the ALICE collaboration in terms of various LHC event generators and IP-Glasma calculations.

Multiplicity and pseudo-rapidity density distributions of charged particles produced in pp, pA and AA collisions at RHIC & LHC energies

Multiplicity and pseudorapidity (η) density (dN ch/dη) distributions of charged hadrons provide key information towards understanding the particle production mechanisms and initial conditions of high-energy heavy-ion collisions. However, detector constraints limit the η-range across which charged particle measurements can be carried out. Extrapolating the measured distributions to large η-range by parameterizing measured distributions and by using calculations from event generators, we characterize the production of charged particles over the full kinematic range. In the present study, we use three different anstze to obtain quantitative descriptions of the shape of pseudorapidity distributions of charged hadrons produced in pp, p–A, and A–A collisions for beam energies () ranging from a few GeV to a few TeV corresponding to RHIC and LHC energies. We study the limiting fragmentation behavior in these collisions and report evidence for participant-scaling violations in high-energy collisions at the TeV scale. We additionally examine measured pseudorapidity distributions to constrain models describing initial conditions of particle production. We predict the centrality dependence of charged particle multiplicity distributions at FAIR and NICA energies and give an estimation of charged particle multiplicity at η = 0 for the proposed HE-LHC and FCC energies.

Modeling charged-particle multiplicity distributions at LHC

With many applications in high-energy physics, Deep Learning or Deep Neural Network (DNN) has become noticeable and practical in recent years. In this article, a new technique is presented for modeling the charged particles multiplicity distribution [Formula: see text] of Proton-Proton [Formula: see text] collisions using an efficient DNN model. The charged particles multiplicity n, the total center of mass energy [Formula: see text], and the pseudorapidity [Formula: see text] used as input in DNN model and the desired output is [Formula: see text]. DNN was trained to build a function, which studies the relationship between [Formula: see text]. The DNN model showed a high degree of consistency in matching the data distributions. The DNN model is used to predict with [Formula: see text] not included in the training set. The expected [Formula: see text] had effectively merged the experimental data and the values expected indicate a strong agreement with Large Hadron Collider (LHC) for ATLAS measurement at [Formula: see text], 7 and 8 TeV.

Inclusive charged and neutral particle multiplicity distributions in χcJ and J/ψ decays

Using a sample of 106 million $\psi(3686)$ decays, $\psi(3686) \to \gamma \chi_{cJ} (J = 0, 1, 2)$ and $\psi(3686) \to \gamma \chi_{cJ}, \chi_{cJ} \to \gamma J/\psi$ $(J = 1, 2)$ events are utilized to study inclusive $\chi_{cJ} \to$ anything, $\chi_{cJ} \to$ hadrons, and $J/\psi \to$ anything distributions, including distributions of the number of charged tracks, electromagnetic calorimeter showers, and $\pi^0$s, and to compare them with distributions obtained from the BESIII Monte Carlo simulation. Information from each Monte Carlo simulated decay event is used to construct matrices connecting the detected distributions to the input predetection "produced" distributions. Assuming these matrices also apply to data, they are used to predict the analogous produced distributions of the decay events. Using these, the charged particle multiplicities are compared with results from MARK I. Further, comparison of the distributions of the number of photons in data with those in Monte Carlo simulation indicates that G-parity conservation should be taken into consideration in the simulation.

Energy dependence of the inelasticity in pp/p{overline{p}} collisions from experimental information on charged particle multiplicity distributions

The dependence of the inelasticity in terms of the center of mass energy is studied in the eikonal formalism, which provides connection between elastic and inelastic channels. Due to the absence of inelasticity experimental datasets, the present analysis is based on experimental information available on the full phase space multiplicity distribution covering a large range of energy, namely 30 < sqrt{s}le 1800 GeV. Our results indicate that the decrease of inelasticity is consequence of minijets production from semihard interactions arising from the scattering of gluons carrying only a very small fractions of the momenta from their parent protons. Alternative methods of estimating the inelasticity are discussed and predictions to the LHC energies are presented.

A look at multiparticle production via modified combinants

As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, P(N), by investigating the so-called modified combinants, C_j, extracted from them. This information is encoded in the observed specific oscillatory behaviour of C_j, which phenomenologically can be described only by some combinations of compound distributions based on the Binomial Distribution. So far this idea has been checked in pp and e^+e^- processes (where observed oscillations are spectacularly strong). In this paper we continue observation of multiparticle production from the modified combinants perspective by investigating dependencies of the observed oscillatory patterns on type of colliding particles, their energies and the phase space where they are observed. We also offer some tentative explanation based on different types of compound distributions and stochastic branching processes.

Compelling Evidence of Oscillatory Behaviour of Hadronic Multiplicities in the Shifted Gompertz Distribution

Study of charged particle multiplicity distribution in high-energy interactions of particles helps in revealing the dynamics of particle production and the underlying statistical patterns, by which these distributions follow. Several distributions derived from statistics have been employed to understand its behaviour. In one of our earlier papers, we introduced the shifted Gompertz distribution to investigate this variable and showed that the multiplicity distributions in a variety of processes at different energies can be very well described by this distribution. The fact that the shifted Gompertz distribution, which has been extensively used in diffusion theory, social networking and forecasting, has been used for the first time in high-energy physics collisions remains interesting. In this paper, we investigate the phenomenon of oscillatory behaviour of the counting statistics observed in the high-energy experimental data, resulting from different types of recurrence relations defining the probability distributions. We search for such oscillations in the multiplicity distributions well described by the shifted Gompertz distribution and look for retrieval of additional valuable information from these distributions.

Multiplicity fluctuations in the Glauber Monte Carlo approach

We discuss multiplicity fluctuations of charged particles produced in nuclear collisions measured event-by-event by the NA49 experiment at CERN SPS within the Glauber Monte Carlo approach. We use the concepts of wounded nucleons and wounded quarks in the mechanism of multiparticle production to characterize multiplicity fluctuations expressed by the scaled variance of multiplicity distribution. Although Wounded Nucleon Model correctly reproduce the centrality dependence of the average multiplicity in Pb+Pb collisions, it completely fails in description of corresponding centrality dependence of scaled variance of multiplicity distribution. Using subnucleonic degrees of freedom, i.e. wounded quarks within Wounded Quark Model, it is possible to describe quite well the multiplicity distribution of charged particles produced in proton+proton interactions. However, the Wounded Quark Model with parameters describing multiplicity distribution of particles produced in proton+proton interactions substantially exceeds the average multiplicity of charged particles produced in Pb+Pb collisions. To obtain values of average multiplicities close to those experimentally measured in Pb+Pb collisions, the concept of shadowed quark sources is implemented. Wounded Quark Model with implemented shadowing source scenario reproduces the centrality dependence of scaled variance of multiplicity distribution of charged particles produced in Pb+Pb collisions in the range from the most central to mid-peripheral interactions.

Glauber model for a small system using the anisotropic and inhomogeneous density profile of a proton

Recent studies reveal that at high energies, collisions of a small system such as $p+p$ gives signatures similar to that widely observed in heavy ion collisions hinting toward the possibility of forming a medium with collective behavior. With this motivation, we have used the Glauber model, which is traditionally applied to heavy ion collisions, in a small system using the anisotropic and inhomogeneous density profile of a proton and found that the proposed model reproduces the charged particle multiplicity distribution of $p+p$ collisions at LHC energies very well. Collision geometric properties such as the mean impact parameter, the mean number of binary collisions ($⟨{N}_{\mathrm{coll}}⟩$), and the mean number of participants ($⟨{N}_{\mathrm{part}}⟩$) at different multiplicities are determined. Having estimated $⟨{N}_{\mathrm{coll}}⟩$, we have calculated the nuclear modificationlike factor (${R}_{\mathrm{HL}}$) in $p+p$ collisions. We also estimated eccentricity and elliptic flow as a function of charged particle multiplicity using the linear response to the initial geometry.

Effects of phase space variables on oscillations of modified combinants

It has been shown recently that additional information can be ob- tained from charged particle multiplicity distribution by investigating their mod- ified combinantsC j, which exhibit periodic oscillatory behaviour. The modified combinants obtained from experimental data can be expressed in a recurrent form involving the probability of obtainingNcharged particlesP(N), scaled by the void probabilityP(0). The effects of various experimental observables such as |η|,pTand centre-of-mass collision energy √son the oscillations ofCjwill be discussed.

Modified combinant analysis of the e+e− multiplicity distributions

As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, [Formula: see text], by extracting information from the modified combinants, [Formula: see text]. This information is encoded in their specific oscillatory behavior, which can be described only by some combinations of compound distributions such as the Binomial Distribution. This idea has been applied to [Formula: see text] and [Formula: see text] processes thus far. In this note, we show that an even stronger effect is observed in the [Formula: see text] deduced from [Formula: see text] collisions. We present its possible explanation in terms of the Generalized Multiplicity Distribution (GMD) proposed some time ago.

Wounded nucleon, quark, and quark-diquark emission functions versus experimental results from the BNL Relativistic Heavy Ion Collider at sNN=200 GeV

Using the wounded nucleon, quark, and quark-diquark models, we extract the wounded source emission functions from the PHOBOS data for d+Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. We apply these models to compute charged particle multiplicity distributions as functions of pseudorapidity for p+p, p+Al, p+Au, d+Au, $^3$He+Au, Cu+Cu, Cu+Au, Au+Au, and U+U collisions at the same energy and compare them with experimental data from the PHOBOS and PHENIX collaborations. In symmetric collisions of heavy nuclei, the obtained distributions differ among the tested models. On the other hand, in asymmetric collisions, all three models give essentially the same distributions. The wounded quark-diquark and quark models are in reasonable agreement with data for all the investigated systems.

Distributions of the charged particles in the electromagnetic showers initiated by 5-1000 GeV electrons in Fe, W and Pb

The results of calculations of the charged particles multiplicity, energy, radial and time distributions in the electromagnetic showers initiated by electrons with energies from 5 to 1000 GeV in Fe, W and Pb are presented. It is shown that the multiplicity distributions are well fitted by the inverse sum of two exponents in a wide range of energy and lead depth. The shapes of energy and radial distributions at the shower maximum weakly depend on the electron energy. Radial distributions for all materials studied are similar if radius is expressed in g/cm2. The time spread of the charged particles at the shower maximum turned out to be in the picosecond range.

Multiplicity distribution and normalized moments in p–p collisions at LHC in forward rapidity using Weibull model

The measured charged particle multiplicity distributions in the forward rapidity region of the p−p collisions at , 7 TeV and 8 TeV at the LHC have been described using the Weibull distribution. The higher order (up to fifth order) normalized moments and the factorial moments are also calculated using the parameters extracted from the distribution. The multiplicity distributions in the forward region are observed to be well described by the Weibull regularity and the higher order moment calculations confirm the violation of KNO scaling that has been observed at mid-rapidity and lower energies in p−p collisions. The Weibull parameters and moments for p−p collisions at are also estimated for the forward region.

Multiplicity Distributions of the Charged Particles at the Maximum of Electromagnetic Showers Initiated by 5–1000 GeV Electrons in Fe, W, and Pb

Charged particles multiplicity distributions at the maximum of electromagnetic showers initiated by 5 to 1000 GeV electrons in Fe, W, and Pb were calculated using GEANT4. It is shown that they are reasonably well fitted by the inverse sum of two exponents and the energy dependence of the average multiplicity follows power law with the power of ~0.95 for all studied materials.

Three-component multiplicity distribution, oscillation of combinants and properties of clans in pp collisions at the LHC

Multiplicity distributions of charged particles measured by the ATLAS Collaboration in proton–proton collisions at sqrt{s}=8 and 13 TeV are analyzed in the framework of a weighted superposition of three negative binomial distribution functions. The examination of the experimental data confirms the existence of a narrow peak at low multiplicities found earlier at sqrt{s}=0.9 and 7 TeV. The peak is described by the third separate component of the total distribution. The energy dependence of the multiplicity characteristics of the three-component scenario is studied. It is demonstrated that the third multiplicity component might be responsible for oscillations of combinants observed lately in the analysis of the multiplicity distributions measured in proton–proton collisions at the LHC. Some consequences of the three-component description of the data for the clan parameters are analyzed.

Multifractal Analysis of Charged Particle Multiplicity Distribution in the Framework of Renyi Entropy

A study of multifractality and multifractal specific heat has been carried out for the produced shower particles in nuclear emulsion detector for16O-AgBr,28Si-AgBr, and32S-AgBr interactions at 4.5AGeV/c in the framework of Renyi entropy. Experimental results have been compared with the prediction of Ultra-Relativistic Quantum Molecular Dynamics (UrQMD) model. Our analysis reveals the presence of multifractality in the multiparticle production process in high energy nucleus-nucleus interactions. Degree of multifractality is found to be higher for the experimental data and it increases with the increase of projectile mass. The investigation of quark-hadron phase transition in the multiparticle production in16O-AgBr,28Si-AgBr, and32S-AgBr interactions at 4.5 AGeV/c in the framework of Ginzburg-Landau theory from the concept of multifractality has also been presented. Evidence of constant multifractal specific heat has been obtained for both experimental and UrQMD simulated data.

Multifractal characteristics of multiparticle production in heavy-ion collisions at SPS energies

Entropy, dimensions and other multifractal characteristics of multiplicity distributions of relativistic charged hadrons produced in ion–ion collisions at SPS energies are investigated. The analysis of the experimental data is carried out in terms of phase space bin-size dependence of multiplicity distributions following the Takagi’s approach. Yet another method is also followed to study the multifractality which, is not related to the bin-width and (or) the detector resolution, rather involves multiplicity distribution of charged particles in full phase space in terms of information entropy and its generalization, Rényi’s order-[Formula: see text] information entropy. The findings reveal the presence of multifractal structure — a remarkable property of the fluctuations. Nearly constant values of multifractal specific heat “[Formula: see text]” estimated by the two different methods of analysis followed indicate that the parameter “[Formula: see text]” may be used as a universal characteristic of the particle production in high energy collisions. The results obtained from the analysis of the experimental data agree well with the predictions of Monte Carlo model AMPT.

Asymptotic Analysis of the parton branching equation at LHC Energies

An asymptotic solution to the QCD parton branching equation is derived using the method of Laplace transformation and saddle point approximation. The distribution is applied to charged particle multiplicity distributions in proton-proton collisions at √s = 0.9, 2.36, and 7 TeV for |ƞ| &lt; 0.5, 1.0, 1.5, 2.0, 2.4, and 8 TeV for |ƞ| &lt; 0.5, 1.0, 1.5, as well as 13 TeV data for |ƞ| &lt; 0.8 and 2.5.

Charged-particle multiplicity distributions over a wide pseudorapidity range in proton-proton collisions at sqrt{s}= 0.9, 7, and 8 TeV

We present the charged-particle multiplicity distributions over a wide pseudorapidity range (-,3.4<eta <5.0) for pp collisions at sqrt{s}= 0.9, 7, and 8 TeV at the LHC. Results are based on information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE, extending the pseudorapidity coverage of the earlier publications and the high-multiplicity reach. The measurements are compared to results from the CMS experiment and to PYTHIA, PHOJET and EPOS LHC event generators, as well as IP-Glasma calculations.