Scaled Factorial Moments Research Articles

Search for the Critical Point via Intermittency Analysis in NA61/SHINE

The existence and location of the QCD critical point are objects of both experimental and theoretical studies. The comprehensive data collected by NA61/SHINE during a two-dimensional scan in beam momentum and system size allows for a systematic search for the critical point – a search for a non-monotonic dependence of various correlation and fluctuation observables on collision energy and size of colliding nuclei. Intermittency analysis is a statistical tool used in heavy ion collisions that includes the study of scaled factorial moments (SFMs) of multiplicity distributions in the 2D transverse momentum space to detect power-law fluctuations and explore different aspects of the QCD phase diagram. In particular, proton intermittency has been used to locate the critical point of strongly interacting matter, and, more recently, intermittency of negatively charged hadrons have also been used to study the properties of QCD interactions.

Scaling properties of particle density fluctuations at LHC energies

The availability of high-multiplicity events at LHC energies provides a unique opportunity to examine the nature of phase-transition (PT) in heavy-ion collisions. Within the framework of HYDJET++ model, a systematic study of particle density fluctuations in narrow phase-space bins in Pb-Pb collisions at and 5.02 TeV energies is performed using the method of scaled factorial moments (SFM). The findings reveal the presence of intermittency in the 2-dimensional (2D) phase space distribution of charged particles at the LHC energies. The anomalous fractal dimensions, d q , are observed to increase with the order of the moments q, suggesting the multifractal nature of the charged particle production. The parameter λ q is found to exhibit a monotonically decreasing trend with the order of the moments but with no clear minima in λ q values. Furthermore, the value of the critical exponent is estimated and compared with those predicted by other models reported at RHIC and LHC energies. The value of the critical exponent, ν, obtained in the present study, shows significant departure from the value ∼1.304, as expected for the Ginzberg-Landau (GL) type second-order PT but exhibits a good level of agreement with the results obtained by other models at LHC energies.

Mixed Factorial Moments in the Nuclear Collisions of 28Si AgBr at 14.6A GeV

A new method has been applied for the study of intermittency in the collisions of 28Si AgBr at 14.6 A GeV for the produced relativistic charged particles by using the method of mixed factorial moment (MFM). In this paper an analysis has been made for the presence of fractal behavior with three different approaches of Scaled factorial Moments (SFMs) named as- horizontal, vertical and mixed (horizontal and vertical together). The non-statistical fluctuations of relativistic charged particles have been calculated on events with different degree of centrality. These results have been compared with the results of simulated data obtained from UrQMD model and we find a good agreement between experimental data and simulated data.

Intermittency Approach in the Nuclear Collisions of 28Si + AgBr at 14.6A GeV - Nuclear Emulsion Experiment a Particle Detector

A new method has been applied for the study of intermittency in the collisions of 28Si + AgBr at 14.6 A GeV for the produced relativistic charged particles by using the method of mixed factorial moment (MFM). In this paper an analysis has been made for the presence of fractal behavior with three different approaches of Scaled factorial Moments (SFMs) named as- horizontal, vertical and mixed (horizontal and vertical together). The non-statistical fluctuations of relativistic charged particles have been calculated on events with different degree of centrality. These results have been compared with the results of simulated data obtained from UrQMD model and we find a good agreement between experimental data and simulated data.

Intermittency Approach in the Nuclear Collisions of 28Si + AgBr at 14.6A GeV - Nuclear Emulsion Experiment a Particle Detector

A new method has been applied for the study of intermittency in the collisions of 28Si + AgBr at 14.6 A GeV for the produced relativistic charged particles by using the method of mixed factorial moment (MFM). In this paper an analysis has been made for the presence of fractal behavior with three different approaches of Scaled factorial Moments (SFMs) named as- horizontal, vertical and mixed (horizontal and vertical together). The non-statistical fluctuations of relativistic charged particles have been calculated on events with different degree of centrality. These results have been compared with the results of simulated data obtained from UrQMD model and we find a good agreement between experimental data and simulated data.

Scaling Nature of Target Fragments in the 28Si-Emulsion Interaction at an Energy of 14.6A GeV

An attempt has been made to study the fractal behavior of the experimental data on nuclear fragments obtained from 28Si-Emulsion collisions at 14.6A GeV. The whole analysis is performed by using two different methods, namely the methods of scaled factorial moments (SFMs), Fq; and multifractal moments, Gq: We have found that the present data reflect a multifractal geometry for nuclear fragments along with the Monte Carlo events (simulated events). Finally, some evidences of non-thermal phase transitions and the scaling law nature of SFMs have been studied.

Systematic study of multiparticle production in nucleus–nucleus interactions at 14.6 A GeV

An experimental analysis of 855 events induced by 14.6 A GeV 28Si in nuclear emulsion is presented. Mean multiplicities of charged secondary particles produced in the nuclear interactions are studied and compared with the results from the other experiments for the same projectile at 3.7 A GeV as well as data for proton at similar energy (14 GeV). An analysis of pseudorapidity densities of target fragments (black and grey particles) is also performed. The behaviour of the KNO scaling law of the multiplicity distribution for shower particles has been examined. In order to accumulate knowledge about the intermittent behaviour of shower particles, the scaled factorial moments (SFMs) are computed in η-space and ϕ-space for a set of data in the 28Si–AgBr events. Furthermore, validity of limiting fragmentation of shower particles produced in central collision events induced by 28Si-emulsion interactions has been tested. A crude estimation for the energy density of the nuclear matter formed in the central collision events at our energy has been examined.

Study of Deconfinement Phase Transition in Heavy Ion Collisions at BNL Energies

Abstract — The Scaled factorial moments (SFMs) of multiplicity distribution are used to study the deconfinement phase transition in high energy heavy-ion collisions. In the present article we studied the Renyi dimensions and multifractal spectrum in the interaction of 28 S-emulsion collisions at 14.6A GeV to investigate non thermal phase transitions during such collisions. Index Terms — Novel state of matter, quark-gluon plasma (QGP), scaled factorial moments (SFMs). I. I NTRODUCTION During last couple of years, different nuclei have been accelerated to relativistic energies and brought to collisions with a great variety of target nuclei. An ultimate aim of studying nucleus – nucleus (A-A) collisions is to investigate for a phenomena connecting with large densities obtained in such nuclear collisions. So due to this one can obtained an opportunity to explore strongly interacting matter at energy densities unprecedented in a laboratory, which eventually gives an evidence for the existence of quark-gluon plasma (QGP). The QGP is a novel state of matter in which quarks and gluons are no longer confined to volumes of hadronic dimensions. In deep inelastic scattering experiments, it has already been revealed that quarks at very short distances move freely, which is referred to as the asymptotic freedom. Quantum Chromo-dynamics (QCD) describes the strong interactions of quarks and gluons [1]. The experimental observation of large rapidity fluctuations in relativistic heavy ion collisions by R. C. Hwa and J. C. Pan [2], [3] using the method of multifractal moments method,

Multidimensional intermittency study of target fragments at CERN SPS energies

An investigation on the presence of ring and jet-like structures is carried out in the angular emission of target-evaporated slow particles emitted in 16O–Ag/Br interactions at 60AGeV/c and 32S–Ag/Br interactions at 200AGeV/c. The nuclear emulsion technique was employed to collect the experimental data. We compared our experimental results with those obtained from Monte Carlo simulations. The analysis indicates the presence of ring and jet-like structures in the experimental data beyond the statistical noise. The presence of ring-like structure is fairly pronounced in 16O–Ag/Br interactions compared to 32S–Ag/Br interactions and jet-like structure is more distinct in 32S. One dimensional (1d) intermittency for ring-like structures and two dimensional (2d) intermittency for jet-like structures are expected. The self-affine behavior of 2d scaled factorial moments (SFM) were investigated and the strength of 2d intermittency was determined. For each set of data, the 2d results were compared with the corresponding one-dimensional (1d) intermittency results. The strength in 2d is significantly greater than 1d for 32S–Ag/Br interactions whereas for 16O–Ag/Br interactions 1d is greater than 2d.This is also a sign of predominance of jets in 32S–Ag/Br and the rings in 16O–Ag/Br interactions.

Ring and jet-like structures and two-dimensional intermittency in nucleus–nucleus collisions at

Abstract We have investigated the presence of ring and/or jet-like structures in the angular emission of secondary charged mesons (shower tracks) coming out of 16O–Ag/Br and 32S–Ag/Br interactions, each at an incident momentum of 200 A GeV / c . Nuclear photographic emulsion technique has been used to collect the experimental data. The experimental results have been compared with the results simulated by Monte Carlo method. The analysis indicates presence of ring and jet-like structures in the experimental data beyond statistical noise. This kind of jet structure is expected to give rise to a strong two-dimensional ( 2 d ) intermittency. The self-affine behaviour of 2d scaled factorial moments (SFM) has therefore been investigated and the strength of 2d intermittency has been determined. For each set of data the 2d results have been compared with the respective one-dimensional ( 1 d ) intermittency results.

Study of Non-Statistical Fluctuations in Relativistic Nuclear Collisions

An attempt is made to study the existence of non-statistical fluctuations of relativistic particles using the method of scaled factorial moments (SFMs) in the interactions of 28 Si and 12 C nuclei ...

INTERMITTENCY IN 4.5A AND 14.5A GeV/c28Si-NUCLEUS INTERACTIONS

The occurrence of intermittent patterns in 14.5 A GeV/c 28 Si -nucleus interactions is examined in terms of Scaled Factorial Moments (SFMs), introduced by Bialas and Peschanski. Further, to examine the dependence of various interesting characteristics of SFMs on incident energy, the data on 4.5 A GeV/c 28 Si -nucleus collisions available in our laboratory are analyzed. Interestingly, log-log plots between rapidity interval δη and the qth order factorial moment Fq for both the energies exhibit linear behavior indicating thereby the presence of intermittency in the interactions investigated. Moreover, to look at the fractal nature of the particle emitting sources, variation of the fractal dimensions, dq with the order of the moment is investigated. Finally, study of the variation of λq [=(ϕq+1)/q)] with the order of the moment, q indicates a possibility of non-thermal phase transition in certain types of events

Intermittency and multifractality of medium-energy particles in proton-nucleus interactions at 800 GeV.

We investigate the intermittent and multifractal behaviors of the multiplicity fluctuations of medium energy particles in 800 GeV proton interactions with emulsion nuclei. For our analysis, we have used ordinary scaled factorial moments (SFM) denoted as ${\mathit{F}}_{\mathit{q}}$, modified SFM, (${\mathit{F}}_{\mathit{q}}^{\ensuremath{'}}$) and modified multifractal moments, (${\mathit{G}}_{\mathit{q}}^{\ensuremath{'}}$) with suppressed statistical contributions. For a close comparison between the ${\mathit{F}}_{\mathit{q}}^{\ensuremath{'}}$ and ${\mathit{G}}_{\mathit{q}}^{\ensuremath{'}}$ moments, they have both been expanded in a set of basic functions each of which has a characteristic fractal behavior as a function of the resolution in phase space. The experimental values of anomalous fractal dimensions ${\mathit{d}}_{\mathit{q}}$ and Renyi dimensions ${\mathit{D}}_{\mathit{q}}$ are determined for q=2-5. The latter are corrected for statistical contamination in the multiplicity fluctuations. The observed variation of ${\mathit{d}}_{\mathit{q}}$ and ${\mathit{D}}_{\mathit{q}}^{\mathrm{dyn}}$ with q supports a self-similar random cascading mechanism for the particle production process. It is found that ${\mathit{D}}_{\mathit{q}}^{\mathrm{dyn}}$+${\mathit{d}}_{\mathit{q}}$=1.

Intermittency and fragmentation of target residue in high-energy nuclear interactions.

We analyze the angular distribution of target-associated slow particles in high-energy nuclear interactions, in terms of scaled factorial moments (SFMs). A power-law type behavior of SFMs, popularly known as ``intermittency,'' is a diagnostic indicator of possible dynamical phenomenon in multiparticle production and multifragmentation processes in high-energy physics. Our data of target associated slow particles reveal similar type of increase in SFMs with decreasing bin width of the angular distribution. The new observation thus contradicts the existing concept of evaporation model that the ``statistical equilibrium'' is reached before the emission of fragmented particles from residual target nuclei at high-energy nuclear interactions.

Dynamical fluctuations in pion pseudorapidity distributions at Bevalac energies

By performing hadronic transport model calculations, we study the reduced scaled factorial moments as a function of the bin size in pseudorapidity for pions produced in oxygen on emulsion reactions at E A =2.1 GeV . The magnitude of the calculated reduced scale factorial moments is compatible with that of the experimental data only by mixing events of widely different impact parameters. The calculated anomalous dimension increases with the increasing rank of the moments, but it is smaller than the experimental data by a factor of 2–5.