Two-pion Correlation Research Articles

Collision energy dependence of source sizes for primary and secondary pions at energies available at the JINR nuclotron-based ion collider facility from Lévy fits

We study the evolution of the two-pion correlation function parameters with collision energy in the context of relativistic heavy-ion collisions within the NICA energy range. To this end, we perform UrQMD simulations in the cascade mode to produce samples of pions from 5×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\ imes 10^6$$\\end{document} Bi+Bi collisions for each of the studied energies. The effects of the quantum-statistical correlations are introduced using the correlation afterburner code CRAB. We fit the correlation function using Gaussian, exponential and symmetric Lévy shapes and show that for all collision energies the latter provides the best fit. We separate the sample into pions coming from primary processes and pions originating from the decay of long-lived resonances, and show that the source size for the latter is significantly larger than for the former. The source size for the secondaries, is similar but in general larger than the size for the whole pion sample. To further characterize the pion source, we also simulate the effects of a non-ideal detector introducing a momentum smearing parameter, representing the minimum pair momentum and thus a maximum source size that can be resolved. The values of the correlation function intercept parameter are therefore modified from the values they attain for the perfect detector case. Using the core-halo picture of the source, we show that the values of the intercept parameter are influenced by the presence of a significant fraction of core pions coming from the decay of long-lived but slow-moving resonances. These findings serve as a benchmark to compare with future Monte Carlo studies that consider an Equation of State and thus allow for a phase transition within the studied energy domain.

Pion Interferometry with Lévy-Stable Sources in sNN = 200 GeV Au + Au Collisions at STAR

Measurements of femtoscopic correlations in high-energy heavy-ion collisions are used to unravel the space–time structure of the particle-emitting source (the quark–gluon plasma). Recent results indicate that the pion pair source exhibits a power law behavior and can be described well by a Lévy distribution. In this study, Lévy fits were applied to the measured one-dimensional two-pion correlation functions in Au + Au collisions at sNN = 200 GeV. The three extracted source parameters are the Lévy scale parameter, R, which relates to the size of the source; the correlation strength parameter, λ; and the Lévy exponent, α, which characterizes the power law tail of the source. In this paper, we report the current status of the analysis of the extracted Lévy source parameters and present their dependence on average transverse mass, mT, and on centrality.

Numerical calculation of 3-pion Coulomb scattering using scalar QED

The Coulomb scattering between three charged pions is shown to be perturbatively calculable using scalar QED for the relative momenta accessible to high-energy experiments of particle collisions. For the triplet relative momenta, Q3≳50 MeV/c, the calculated three-pion correlation function at O(α2) is very similar to the commonly-used triple-product of pair factors—Riverside approximation. At lower Q3, but above the lowest existing experimental measurement of ∼15 MeV/c, terms of O(α3) or higher are needed to obtain a convincing description of three-pion Coulomb interactions. This is in contrast to two-pion correlations, for which the known exact solution is shown to be saturated by the lower orders at comparable pair relative momenta.

Investigating Effect of Coherent Emission Length on Pion Interferometry in High-Energy Collisions Using a Multiphase Transport Model

We study the two-pion Hanbury Brown–Twiss correlation functions for a partially coherent source constructed with the emission points and momenta of the identical pions generated by a multiphase transport model. A coherent emission length is introduced, the effects of which on the two-pion interferometry results in central Au-Au collisions at sNN=200 GeV, central Pb-Pb collisions at sNN=2.76 TeV, and p-p collisions at s=13 TeV are investigated. It is found that the effect of coherent emission length reduces the two-pion correlation functions in the nucleus–nucleus collisions, leading to an average decrease of chaoticity parameter by approximately 15% in the high transverse momentum range. However, the influence of coherent emission length on the two-pion correlation functions in the p-p collisions is small, while the effect of coherent emission length on the chaoticity parameter is almost independent of the transverse momentum of pion pair in the p-p collisions.

Finite volume and magnetic field effects on the two-pion correlation function in relativistic heavy-ion collisions

We study the combined effects of a finite volume and an external magnetic field on the charged two-pion correlation function. For these purposes, we consider a dilute system of pions where the finite volume effects are introduced computing the pion wave functions with rigid boundary conditions in a cylindrical geometry in the presence of a uniform and constant magnetic field. We find that for slow pions, namely, for the case where the average pair momentum is small, the correlation function shows a large distortion, as opposed to the case where the average pair momentum is large. For a finite density system, the intercept of the correlation function is reduced, signaling the increasing importance of the pion ground state contribution. An increasing strength of the magnetic field reduces the importance of the ground state and the intercept becomes closer to 2.

Exploring hot and dense QCD matter with HADES

Experiments at snn 3 GeV provide the lowest energy point of the global effort made by the heavy-ion community in order to map the QCD phase diagram. This correspond to the highest baryon chemical potential, 700-900 MeV according to the universal freeze-out curve, and temperatures of the fireball of 60-80 MeV. The formed matter can be characterized in terms of particle spectra, fluctuations and correlations. The dilepton spectrum is dominated by thermal emission from the medium and it is sensitive to in medium hadron properties. Strangeness production occurs below the free nucleon-nucleon threshold and it is a sensitive probe to test models of strangeness propagation in matter and its coupling to baryons. Data show a common scaling of measured yields as a function of number of participating nucleons independently on the strangeness content or mass of the hadron. Strangeness propagation in cold nuclear matter produced in pion induced reactions on heavy and light targets shows a significant absorption of negative kaons in heavy targets as well as a similar behaviour of ϕ indicating a strong coupling of ϕ with nucleons. Two-pion correlations, flow harmonics, fluctuations are explored as well in order to further pin down the properties of the created matter.

Shape Analysis of HBT Correlations at STAR

To study the nature of the quark-hadron phase transition, it is important to investigate the space-time structure of the hadron-emitting source in heavy-ion collisions. Measurements of HBT correlations have proven to be a powerful tool to gain information about the source. In these proceedings, we report the current status of the analysis of source parameters obtained from L\'evy fits to the measured one-dimensional two-pion correlation functions in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Two-pion Bose-Einstein Correlations data analysis for the CMS Pb-Pb nucleon collisions

From the data collected in the Compact Muon Solenoid (CMS) Pb-Pb nucleon collisions experiment, the two-pion Bose-Einstein correlation functions for different combination of same charges and different charges are plotted. The influence of repulsion and attraction through Coulomb interaction between charged pions is reduced after applying the standard Gamow-factor Coulomb correction on Gaussian function C(Qinv). According to the Yano-koonin-Podgoretski parametrization, the five-dimensional components of the invariant momentum difference between two pions are calculated. One of the five components, the momentum difference in the transverse plane QT, can be further divided into Qside and Qout. Q0, Qlong, Qside and Qout were then separately plotted and fitted with the Gaussian function. The sizes of pion source or the effective interferometric source can be extracted from the fitting finally.

Geometric Aspects and Some Uses of Deformed Models of Thermostatistics

We consider diverse deformed Bose gas models (DBGMs) focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called μ -deformed Bose gas model ( μ -DBGM), main thermodynamic aspects are treated: total number of particles, deformed partition function, etc. Using a geometric approach, we confirm the existence of critical behavior—Bose-like condensation; we find the critical temperature T c ( μ ) depending on μ so that T c ( μ ) > T c ( Bose ) for μ > 0 . This fact and other advantages of μ -DBGM relative to the usual Bose gas, e.g., stronger effective inter-particle attraction (controlled by the parameter μ ), allow us to consider the condensate in μ -DBGM as a candidate for modeling dark matter. As another, quite successful application we discuss the usage of the two-parameter ( μ ˜ , q )-deformed BGM for effective description of the peculiar (non-Bose like) behavior of two-pion correlations observed in the STAR experiment at RHIC (Brookhaven). Herein, we point out the transparent role of the two deformation parameters μ ˜ and q as being responsible for compositeness and (effective account of) interactions of pions, respectively.

The sigma meson from lattice QCD with two-pion interpolating operators

In this paper, we describe our studies of the sigma meson, [Formula: see text], using two-pion correlation functions. We use lattice quantum chromodynamics in the quenched approximation with so-called clover fermions. By working at unphysical pion masses we are able to identify a would-be resonance with mass less than [Formula: see text], and then extrapolate to the physical point. We include the most important annihilation diagram, which is “partially disconnected” or “single annihilation”. Because this diagram is quite expensive to compute, we introduce a somewhat novel technique for the computation of all-to-all diagrams, based on momentum sources and a truncation in momentum space. In practice, we use only [Formula: see text] modes, so the method reduces to wall sources. At the point where the mass of the pion takes its physical value, we find a resonance in the [Formula: see text] two-pion channel with a mass of approximately [Formula: see text] MeV, consistent with the expected properties of the sigma meson, given the approximations we are making.

A study of event mixing for two-pion Bose-Einstein correlations in the γP → π0π0p reaction

A study of event mixing for two-pion Bose-Einstein correlations in the γP → π0π0p reaction

A study of event mixing for two-pion Bose–Einstein correlations in the γp→π0π0p reaction

We develop an event mixing technique with a missing mass consistency (MMC) cut and a pion energy (PE) cut for the measurement of two-pion Bose-Einstein correlations (BEC) in reactions with only two identical pions produced in the final state. A multi mixing mode that allows one event to be mixed with multiple other events is proposed for the purpose of improving the statistics of mixed samples, and compared with the single mixing mode which requires one original event can be mixed only once. Numerical tests using the {\gamma}p -> {\pi}^0 {\pi}^0 p events are used to testify its ability to measure two-pion correlations. To improve the mixing speed, the optimal MMC cut window is also explored via simulations.

PHENIX results on fluctuations and Bose–Einstein correlations in Au + Au collisions from the RHIC Beam Energy Scan

The RHIC Beam Energy Scan focuses on mapping the QCD phase diagram and pinpointing the location of a possible critical end point. Bose-Einstein correlations and event-by-event fluctuations of conserved quantities, measured as a function of centrality and collision energy, are promising tools in these studies. Recent lattice QCD and statistical thermal model calculations predict that higher-order cumulants of the fluctuations are sensitive indicators of the phase transition. Products of these cumulants can be used to extract the freeze-out parameters [A. Bazavov et al., Phys. Rev. Lett. 109, 192302 (2012)] and to locate the critical point [M. A. Stephanov, K. Rajagopal and E. V. Shuryak, Phys. Rev. D 60, 114028 (1999)]. Two-pion interferometry measurements are predicted to be sensitive to potential softening of the equation of state and prolonged emission duration close to the critical point [S. Pratt, Phys. Rev. Lett. 53, 1219 (1984)]. We present recent PHENIX results on fluctuations of net-charge using high-order cumulants and their products in Au+Au collisions at sNN=7.7–200 GeV, and measurement of two-pion correlation functions and emission-source radii in Cu+Cu and Au+Au collisions at several beam energies. The extracted source radii are compared to previous measurements at RHIC and LHC in order to study energy dependence of the specific quantities sensitive to expansion velocity and emission duration. Implications for the search of a critical point and baryon chemical potentials at various collision energies are discussed.

Techniques for multiboson interferometry

The quantum statistics (QS) correlations of identical bosons are well known to be sensitive to the space-time extent and dynamics of the particle emitting source in high-energy collisions. While two-pion correlations are most often experimentally measured, the QS correlations of three-pions and higher are rarely explored. We present a set of techniques to isolate and analyze 3- and 4-pion QS correlations. In particular, the technique of built correlation functions allows one to more easily study the effects of quantum coherence at finite relative momenta instead of at the unmeasured intercept of correlation functions.

Correlation function intercepts for [formula omitted]-deformed Bose gas model implying effective accounting for interaction and compositeness of particles

In the recently proposed two-parameter μ˜,q-deformed Bose gas model (Gavrilik and Mishchenko, 2013) [3], aimed to take effectively into account both compositeness of particles and their interaction, the μ˜,q-deformed virial expansion of the equation of state (EOS) was obtained. In this paper we further explore the μ˜,q-deformation, namely the version of μ˜,q-Bose gas model involving deformed distributions and correlation functions. In the model, we explicitly derive the one- and two-particle deformed distribution functions and the intercept of two-particle momentum correlation function. The results are illustrated by plots, and the comparison with known experimental data on two-pion correlation function intercepts extracted in RHIC/STAR experiments is given.

Freeze-out radii extracted from three-pion cumulants in pp, p–Pb and Pb–Pb collisions at the LHC

In high-energy collisions, the spatio-temporal size of the particle production region can be measured using the Bose–Einstein correlations of identical bosons at low relative momentum. The source radii are typically extracted using two-pion correlations, and characterize the system at the last stage of interaction, called kinetic freeze-out. In low-multiplicity collisions, unlike in high-multiplicity collisions, two-pion correlations are substantially altered by background correlations, e.g. mini-jets. Such correlations can be suppressed using three-pion cumulant correlations. We present the first measurements of the size of the system at freeze-out extracted from three-pion cumulant correlations in pp, p–Pb and Pb–Pb collisions at the LHC with ALICE. At similar multiplicity, the invariant radii extracted in p–Pb collisions are found to be 5–15% larger than those in pp, while those in Pb–Pb are 35–55% larger than those in p–Pb. Our measurements disfavor models which incorporate substantially stronger collective expansion in p–Pb as compared to pp collisions at similar multiplicity.

Source function extracted from single-event HBT correlation functions of hydrodynamical sources

We investigate the single-event two-pion correlation functions for the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by the Heavy Ion Jet Interaction Generator (HIJING). Using a three-dimension fast Fourier transform (FFT), we further extract the source functions from the single-event correlation functions. It is found that the inhomogeneity of the hydrodynamic sources with the fluctuating initial conditions lead to event-by-event fluctuations of the correlation functions and source functions.

Two- and three-pion quantum statistics correlations in Pb-Pb collisions atsNN=2.76 TeV at the CERN Large Hadron Collider

Correlations induced by quantum statistics are sensitive to the spatio-temporal extent as well as dynamics of particle emitting sources in heavy-ion collisions. In addition, such correlations can be used to search for the presence of a coherent component of pion production. Two and three-pion correlations of same and mixed-charge are measured at low relative momentum to estimate the coherent fraction of charged pions in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC with ALICE. The genuine three-pion quantum statistics correlation is found to be suppressed relative to the two-pion correlation based on the assumption of fully chaotic pion emission. The suppression is observed to decrease with triplet momentum. The observed suppression at low triplet momentum may correspond to a coherent fraction in charged pion emission of 23% $\pm$ 8%.

Femtoscopic and Nonfemtoscopic Two-Particle Correlations inA+Aandp+pCollisions at RHIC and LHC Energies

The theoretical review of the last femtoscopy results for the systems created in ultrarelativisticA+A,p+p, andp+Pbcollisions is presented. The basic model, allowing to describe the interferometry data at SPS, RHIC, and LHC, is the hydrokinetic model. The model allows one to avoid the principal problem of the particlization of the medium at nonspace-like sites of transition hypersurfaces and switch to hadronic cascade at a space-like hypersurface with nonequilibrated particle input. The results for pion and kaon interferometry scales inPb+PbandAu+Aucollisions at LHC and RHIC are presented for different centralities. The new theoretical results as for the femtoscopy of small sources with sizes of 1-2 fm or less are discussed. The uncertainty principle destroys the standard approach of completely chaotic sources: the emitters in such sources cannot radiate independently and incoherently. As a result, the observed femtoscopy scales are reduced, and the Bose-Einstein correlation function is suppressed. The results are applied for the femtoscopy analysis ofp+pcollisions ats=7 TeV LHC energy andp+Pbones ats=5.02 TeV. The behavior of the corresponding interferometry volumes on multiplicity is compared with what is happening for centralA+Acollisions. In addition the nonfemtoscopic two-pion correlations in proton-proton collisions at the LHC energies are considered, and a simple model that takes into account correlations induced by the conservation laws and minijets is analyzed.

Deciphering nonfemtoscopic two-pion correlations inp+pcollisions with simple analytical models

A simple model of nonfemtoscopic particle correlations in proton-proton collisions is proposed. The model takes into account correlations induced by the conservation laws as well as correlations induced by minijets. It reproduces well the two-pion nonfemtoscopic correlations of like-sign and unlike-sign pions in proton-proton collision events at $\sqrt{s} = 900$ GeV analyzed by the ALICE Collaboration. We also argue that similar nonfemtoscopic correlations can appear in the hydrodynamic picture with event-by-event fluctuating nonsymmetric initial conditions that are typically associated with nonzero higher-order flow harmonics.