Search

This work analyzes the $$SePaC$$ method of fractals and various background events (mixed, random, and distributed according to Gauss’s law, as well as by power and exponential laws) in order to search and reconstruct fractal structures. It is shown that some of the background events are reconstucted as fractals. Dimensional distributions of various events are considered. It is found that these distributions for fractals and background events are different. Characteristics are proposed that describe the features of fractal structures. They are compared for fractals and background events. Criteria for background suppression are proposed and the results of their application are presented. It is found that the application of the criteria changes the distribution of background events by dimension, and the use of a combination of criteria suppresses the background.

Results of a new analysis of negative particle yields in Au + Au collisions obtained by the STAR Collaboration in the first phase of the RHIC Beam Energy Scan (BES) program in the framework of $$z$$ -scaling approach are presented. The spectra were measured over a wide range of collision energy $$\sqrt {{{s}_{{NN}}}} = 7.7 - 200$$ GeV and transverse momentum of produced particles for different centralities at $$\left| \eta \right| < 0.5.$$ The concept of the $$z$$ -scaling based on self-similarity, locality, and fractality of hadron interactions at a constituent level is verified. The constituent energy loss as a function of energy and centrality of collision and transverse momentum of inclusive particle was estimated.

$z$-Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated. The scaling for negative particle production in $Au+Au$ collisions from BES-I program at RHIC is demonstrated. The scaling variable $z$ depends on the momentum fractions of the colliding objects carried by the interacting constituents, and on the momentum fractions of the fragmenting objects in the scattered and recoil directions carried by the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final state are expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function $\psi(z)$ reveals energy, angular, multiplicity, and flavor independence. It has a power behavior at high $z$ (high $p_T$). Based on the entropy principle and $z$-scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated. New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed., Comment: 19 pages, 9 figures; Presented at the 40th International Conference on High Energy Physics, ICHEP2020

The STAR experiment provides measurements of single and double-spin asymmetries in longitudinally and transversely polarized p + p collisions at \(\sqrt s \) = 200 and 510 GeV to deepen our understanding on the proton spin structure and dynamics of parton interactions over a wide range of collision energy, momentum and rapidity of the various produced probes. Polarized processes with W± production allow us to study the spin-flavor structure of the proton. Recent results obtained by STAR on the double longitudinal asymmetry, ALL, of pion and jet production at \(\sqrt s \) = 200 and 510 GeV, the single longitudinal, AL, and transverse, AN, asymmetry of W± production at \(\sqrt s \) = 510 GeV are overviewed. STAR results on azimuthal single transverse asymmetry of pion in p↑ + (p, Au) and jet + π± in p↑ + p collisions are discussed. The proposed Forward Calorimeter System (FCS) and Forward Tracking System (FTS) upgrades at STAR would significantly improve the capabilities of existing detectors for measurements of observables such as asymmetries of pion, jet, Drell-Yan pairs produced at forward rapidities.

An analysis of a data set containing fractals and background events is carried out using the method of the equation system of P-adic coverings (SePaC) and by the box-counting (BC) method. The peculiarities of these methods applied to the search for fractals in sets containing only fractals and background events are studied. Procedures allowing one to establish the presence of fractals, estimate their number in the initial set, separate fractals, and evaluate the portion of background events in the extracted set are suggested. A comparison of the result of an analysis of mixed events by these methods is carried out.

We present new results of analysis of top-quark differential cross sections obtained by the CMS Collaboration in pp collisions in the framework of the z-scaling approach. The spectra are measured over a wide range of collision energy $$\sqrt s = 7,8,13TeV$$ and transverse momentum p T = 30−500 GeV/c of top-quark using leptonic and jet decay modes. Flavor independence of the scaling function ψ(z) is verified in the new kinematic range. The results of analysis of the top-quark spectra obtained at the LHC are compared with similar spectra measured in $$\overline p p$$ collisions at the Tevatron energy $$\sqrt s = 1.96TeV$$ . A tendency to saturation of ψ(z) for the process at low z and a power-law behavior of ψ(z) at high z is observed. The measurements of high-p T is observed. The measurements of highspectra of the top-quark production at highest LHC energy is of interest for verification of self-similarity of particle production, understanding flavor origin and search for new physics symmetries with top-quark probe.

A two-step procedure for the analysis of different-type fractals is proposed for the PaC and SePaC methods. An advantage of the two-step procedures of the PaC and SePaC methods over the basic and modified PaC and SePaC methods is shown. Results of comparative analysis of the unified data set using different approaches (the BC method and two-step procedures of the PaC and SePaC methods) are given. It is shown that the two-step procedure of the SePaC method is most efficient in reconstructing the overall data set.

The space—time properties in the general theory of relativity, as well as the discreteness and non-Archimedean property of space in the quantum theory of gravitation, are discussed. It is emphasized that the properties of bodies in non-Archimedean spaces coincide with the properties of the field of P-adic numbers and fractals. It is suggested that parton showers, used for describing interactions between particles and nuclei at high energies, have a fractal structure. A mechanism of fractal formation with combined partition is considered. The modified SePaC method is offered for the analysis of such fractals. The BC, PaC, and SePaC methods for determining a fractal dimension and other fractal characteristics (numbers of levels and values of a base of forming a fractal) are considered. It is found that the SePaC method has advantages for the analysis of fractals with combined partition.

We present results of analysis of negative particle spectra in A u + A u collisions obtained by the STAR Collaboration in the first phase of the Beam Energy Scan program at RHIC using the z-scaling approach. The spectra were measured over a wide range of collision energy s N N = 7.7 –200 GeV and transverse momentum of produced particles for different centralities in the pseudo-rapidity range | η | 0.5 . A scaling behavior of the spectra as a function of the collision energy and centrality in z-presentation is observed. The concept of the z-scaling based on fundamental principles of self-similarity, locality, and fractality of hadron interactions at high energies is considered. The energy loss as a function of the energy and centrality of the collision and the transverse momentum of inclusive particle is estimated. New indication on self-similarity of fractal structure of nuclei and fragmentation processes with negative particles produced in A u + A u collisions at RHIC is found.

Self-similarity of jet production in polarized p + p collisions is studied. The concept of z-scaling is applied for description of proton spin. New data on the double longitudinal spin asymmetry, ALL, of inclusive jets produced in proton-proton collisions at √s = 200 GeV measured by the STAR Collaboration at RHIC are analyzed in the framework of z-scaling approach. A hypothesis of self-similarity and fractality of the proton spin structure are formulated. A possibility to extract information on spin-dependent fractal dimensions of proton from the asymmetry of jet production is justified. The spin-dependent fractal dimension of proton in process \(\vec p + \vec p \to jet + X\) is estimated.

Search for signatures of phase transition in Au + Au collisions is in the heart of the heavy ion program at RHIC. Systematic study of particle production over a wide range of collision energy revealed new phenomena such as the nuclear suppression effect expressed by nuclear modification factor, the constituent quark number scaling for elliptic flow, the “ridge effect” in Δϕ-Δη fluctuations etc. To determine the phase boundaries and location of the critical point of nuclear matter the Beam Energy Scan (BES-I) program at RHIC has been suggested and performed by STAR and PHENIX Collaborations. The obtained results shown that the program (BES-II) should be continued. In this paper a proposal to use hard cumulative processes in BES Phase-II program is outlined. Selection of the cumulative events is assumed to enrich data sample by new type of collisions characterized by higher energy density and more compressed matter. This would allow finding clearer signatures of phase transition, location of a critical point and studying extreme conditions in heavy ion collisions.

The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized protons at the planned Spin Physics Detector NICA in Dubna. Hypotheses of self-similarity and fractality of the proton spin structure are discussed. The possibilities to extract information on spin-dependent fractal dimensions of hadrons and fragmentation process from asymmetries and coefficients of polarization transfer are justified. The double longitudinal spin asymmetry ALL of π0 meson production and the coefficient of the polarization transfer DLL of Λ hyperon production in proton-proton collisions measured at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimensions of proton and fragmentation process with polarized λ hyperon are estimated. A study of the spin-dependent constituent energy loss as a function of transverse momentum of the inclusive hadron and collision energy is suggested.

Properties of self-similarity and fractality in the processes of interactions of hadrons and nuclei at high energies are discussed. Different methods of fractal analysis (the box counting BC , system of the equations of p-adic coverage S ePaC methods) are described. Fractal analysis of mixed events was carried out by BC and S ePaC methods. The procedure of separation of fractals and background, estimation of the number of fractals in the original data set and contamination of the extracted data was proposed. The dependence of event contamination on multiplicity and background is studied. Reconstruction of the spectrum of fractal dimensions is found to depend on the method and background.

New results of analysis of top -quark differential cross sections obtained by the CMS and ATLAS Collaborations in pp collisions at the LHC in the framework of z -scaling approach are presented. The spectra are measured over a wide range of collision energy √s = 7, 8, 13 TeV and transverse momentum pT = 30−1000 GeV/c of top -quark using leptonic and jet decay modes. The LHC data on transverse momentum of the top -quark spectra are compared with the Tevatron data obtained by the D∅ Collaboration in pp collisions at√s = 1.96 GeV. Flavour independence of the scaling function ψ (z ) in pp and pp interactions over a wide collision energy range√s = 19 − 13000 GeV is verified. This property of ψ (z ) was found for different hadrons from π -meson up to ϒ particle. The flavour independence of ψ (z ) is used as indication on self-similarity of top -quark production. A tendency to saturation of ψ (z ) at low z for top -quark is demonstrated. We anticipate that data on low- and high-pT inclusive spectra of top -quark production at LHC energies could be of interest for verification of the self-similarity over a wide range of masses and different flavour content of produced particles.

New data on inclusive transverse momentum spectra of charged hadrons produced in p + A collisions at U70 are analyzed in the framework of the z-scaling approach. Self-similarity of the hadron production in the high-p T cumualtive region is verified. Scaling function ψ(z) for C, Al, Cu, W nuclei is constructed. It is expressed via the invariant cross section and the average multiplicity density of charged particles. Results of analysis are compared with the data obtained by J. Cronin, R. Sulyaev and D.Jaffe groups. Self-similarity of the hadron production in p + A collisions over a wide kinematical range is verified. A microscopic scenario of p + A interactions in terms of momentum fractions x 1, x 2 is discussed. Indication on self-similarity of the high-p T cumulative hadron production in p + A collisions over a wide kinematical range has been found. Based on the universality of the shape of the scaling function the inclusive cross sections of h − and h + hadrons produced in p + A collisions on C, Al, Cu, W targets in the high-p T deep-cumulatice region are predicted.

The experimental data on inclusive spectra of the π+ mesons produced in p + A collisions at the incident proton momentum of 400 GeV/c obtained by G. Leksin group at FNAL are analyzed in the framework of z-scaling. Self-similarity of the hadron production in the low-pT cumulative region is verified. Scaling function ψ(z) for the Li, Be, C, Al, Cu, Ta nuclei is constructed. It is expressed via the invariant cross section and average multiplicity density of charged particles. Results of the analysis of the low-pT data are compared with the high-pT data sets obtained by J. Cronin, R. Sulyaev and D. Jaffe groups. A microscopic scenario of p + A interactions in terms of momentum fractions x1, x2 is discussed. Indication on self-similarity of the cumulative pion production in p + A collisions over a wide kinematical range has been found. Based on the universality of the shape of the scaling function the inclusive cross sections of the π+ mesons produced in p + A collisions on the Li, Be, C, Al, Cu, Ta targets in deep-cumulative region (x2 ≫ 1/A) are predicted.

Negative particle yields in Au + Au collisions obtained by the STAR Collaboration from BES-I at RHIC are analyzed in the framework of the z-scaling approach. The spectra were measured over a wide range of collision energy $\sqrt {{s_{NN}}} = 7.7 - 200\,{\rm{GeV}}$ and transverse momentum of produced particles for different centralities at $\left| \eta \right| \lt 0.5$. The scaling behavior of the spectra as a function of the collision energy and centrality in z-presentation is verified. The constituent energy loss in dependence on the energy and centrality of collision and transverse momentum of inclusive particle is estimated. New indication on self-similarity of fractal structure of nuclei and fragmentation process is found. A discontinuity of the model parameters - fractal and fragmentation dimensions and specific heat - is considered from the point of view of a phase transition in nuclear matter.

The S ePaC and BC methods are used in the fractal analysis of mixed events containing incomplete fractals. The reconstruction of the event distribution by the dimension DF is studied. The procedures of analyzing incomplete fractals and correcting the determination of DF of combined fractals by the SePaC method are proposed. We find that the S ePaC method fully reconstructs incomplete fractals and suppresses background, the separation of the incomplete fractals and the background by the BC method depends on the basis of the formation of the fractal, and the distribution of events by the value of DF is more accurately reconstructed with the S ePaC method in comparison with the BC method.

The notion of dimension as a quantitative characteristic of space geometry is discussed. It is supposed that hadrons created in interactions between particles and nuclei can be considered sets of points possessing fractal properties in the three-dimensional phase space (pT, η, ϕ). The Hausdorff-Besicovich dimension DF is considered the most natural characteristic for determining the fractal dimension. Different methods for determining the fractal dimension are compared: box counting (BC), P-adic coverage (PaC), and system of equations of P-adic coverage (SePaC). A procedure for choosing optimum values of parameters of the considered methods is presented. These parameters are shown to be able to reconstruct the fractal dimension DF, number of levels Nlev, and fractal structure with maximal efficiency. The features of the PaC- and SePaC-methods in the analysis of fractals with independent branching are noted.

Concept of the dimension of space-time in the general relativity theory and quantum theory is discussed. It is emphasized that the dimension of a discrete space can be defined based on the Hausdorff measure. The noninteger dimension is a typical characteristic of a fractal. The process of hadron formation in interactions between high-energy particles and nuclei is supposed to possess fractal properties. The following methods for analyzing fractals are considered: box counting (BC), method of P-adic coverages (PaC), and method of systems of equations of P-adic coverages (SePaC), for determining the fractal dimension. A comparative analysis of fractals with dependent branching is performed using these methods. We determine the optimum values of parameters permitting one to determine the fractal dimension DF, number of levels Nlev, and the fractal structure with maximal efficiency. It is noted that the SePaC method has advantages in analyzing fractals with dependent branching.

Self-similarity in high-energy multiparticle production processes is discussed. A parton shower and hadronization are assumed to give rise to a set of particle with a fractal structure. It is noted that the box counting (BC) and P-adic coverage (PaC) methods determine the fractal dimension with permissible 1/k ranges. A new method of systems of equations of P-adic coverages (SePaC) is proposed that extends the PaC method to fractals with permissible m/k ranges. The SePaC method is shown to determine the fractal dimension of a shower with a prescribed accuracy, the number of fractal levels, the type of the cascade (random or regular), and its structure.

This paper presents the results of analysis of the D? 1.0 fb-1 data on top-quark differential cross section measurements at the Fermilab Tevatron collider at √s= 1960 GeV in the framework of z-scaling approach. The flavor independence of scaling function Ψ(z)observed in pp and pp interactions over a wide collision energy range √s= 19-1960 GeV has been verified. This property of Ψ(z) was found for different hadrons – from π-mesons up to Υ particles. The flavor independence of Ψ(z) is used as indication on self-similarity of the top-quark production. A tendency to saturation of Ψ(z) at low z for top-quark production has been confirmed. Momentum fraction x1 of the incoming (anti)protons as a function of the scaled transverse momentum pT/m and masses of heavy mesons is studied. We anticipate that the data on low- and high-pT inclusive spectra of the top-quark production at the Tevatron and LHC energies could be of interest to verify self-similarity over a wide range of masses and different flavor content of produced particles.

Self-similarity in multiple processes at high energies is considered. It is assumed that a parton cascade transforms into a hadron shower with a fractal structure. The box counting (BC) method used to calculate the fractal dimension is analyzed. The parton shower with permissible 1/3 parts of pseudorapidity space, which corresponds to a triadic Cantor set, was used as a test fractal. It was found that there is an optimal set of bins (a parameter of the BC method) that allows one to find the fractal dimension with maximal accuracy. The optimal set of bins is shown to depend on the fractal generation law. The P-adic coverage (PaC) method is proposed and used in the fractal analysis. This method makes it possible to determine the fractal dimension of a shower as accurately as possible, the number of fractal levels and partons at each branching point during the parton shower evolution, the type of cascade (either random or regular), and its structure. It is shown to be applicable to an analysis of the regular and random N-ary cascades with permissible 1/k parts of the space studied.

This paper is devoted to experimental study of the instantaneous and average flow structure in the pre-mixed propaneair swirling flames using optical noncontact PIV (Particle Image Velocimetry) method in stereoscopic configuration. A visualization of the typical regimes of combustion for the swirling and non-swirling flame in a wide range of Reynolds numbers and equivalence ratios is presented. In addition, boundaries of steady combustion are defined. Measurements of instantaneous velocity fields for typical combustion regimes are performed. Instantaneous velocity fields were used to calculate the spatial distribution of the mean velocity and turbulence kinetic energy component. Interaction of the flame with a large-scale vortex structures is studied. It shows significantly different effects of burning on the turbulent structure of twisted jet. The paper describes algorithms of data processing, in particular, adaptive cross-correlation method of calculating the instantaneous velocity fields based on an analysis of the local particle image concentration. This method allows to effectively filtering out the velocity vector outliers, which appear in areas with low concentration of tracers during gas flows diagnostics, and calculate the spatial distribution of such characteristics as the intensity of turbulent pulsations.

We present the spectra of negative charged particle production in Au+Au collisions from STAR for the first phase of the RHIC Beam Energy Scan Program measured over a wide range of collision energy sqrt s{NN}=7.7-200 GeV, and transverse momentum of produced particle in different centralities at |eta, 13 pages, LaTeX, 16 figures, Presented at the International Conference "HADRON STRUCTURE'15", 29 June -- 3 July, 2015, Horny Smokovec, Slovak Republic. Preprint JINR E1-2015-83

The recent STAR heavy-ion results obtained in the first phase of the RHIC Beam Energy Scan program are presented. The measurements of particle spectra have been performed over a wide range of collision energy √sNN =7.7-200 GeV, centrality and transverse momentum of produced particles. The fixed target mode in heavy-ion collisions at the STAR experiment also extends considerably the range of search for the new physics. Heavy quarks provide an exceptional probe in understanding properties of the hot and dense medium created in such collisions. The Heavy Flavor Tracker (HFT) and Muon Telescope Detector (MTD) upgrades at the STAR experiment at RHIC significantly improved the experimental capabilities of TPC, ToF and EMC detectors in measuring both open and hidden heavy flavor hadrons in heavy-ion collisions.

Parity-odd domains, corresponding to non-trivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the orbital momentum of the system created in non-central collisions. To study this effect, we investigate a three particle mixed harmonics azimuthal correlator which is a \P-even observable, but directly sensitive to the charge separation effect. We report measurements of this observable using the STAR detector in Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}}$=200 and 62~GeV. The results are presented as a function of collision centrality, particle separation in rapidity, and particle transverse momentum. A signal consistent with several of the theoretical expectations is detected in all four data sets. We compare our results to the predictions of existing event generators, and discuss in detail possible contributions from other effects that are not related to parity violation., Comment: 17 pages, 14 figures, as accepted for publication in Physical Review C.

We present the first measurements of identified hadron production, azimuthal anisotropy, and pion interferometry from Au + Au collisions below the nominal injection energy at the BNL Relativistic Heavy-Ion Collider (RHIC) facility. The data were collected using the large acceptance solenoidal tracker at RHIC (STAR) detector at root s(NN) = 9.2 GeV from a test run of the collider in the year 2008. Midrapidity results on multiplicity density dN/dy in rapidity y, average transverse momentum , particle ratios, elliptic flow, and Hanbury-Brown-Twiss (HBT) radii are consistent with the corresponding results at similar root s(NN) from fixed-target experiments. Directed flow measurements are presented for both midrapidity and forward-rapidity regions. Furthermore the collision centrality dependence of identified particle dN/dy, , and particle ratios are discussed. These results also demonstrate that the capabilities of the STAR detector, although optimized for root s(NN) = 200 GeV, are suitable for the proposed QCD critical-point search and exploration of the QCD phase diagram at RHIC.

Charged-particle spectra associated with direct photon ($\gamma_{dir} $) and $\pi^0$ are measured in $p$+$p$ and Au+Au collisions at center-of-mass energy $\sqrt{s_{_{NN}}}=200$ GeV with the STAR detector at RHIC. A hower-shape analysis is used to partially discriminate between $\gamma_{dir}$ and $\pi^0$. Assuming no associated charged particles in the $\gamma_{dir}$ direction (near side) and small contribution from fragmentation photons ($\gamma_{frag}$), the associated charged-particle yields opposite to $\gamma_{dir}$ (away side) are extracted. At mid-rapidity ($|\eta, Comment: submitted to Phys. Rev. Lett, 6 pages, 4 figures