Two-pion Correlation Functions 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.

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.

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.

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.

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.

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.

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.

Femtoscopy ofppcollisions ats=0.9and 7 TeV at the LHC with two-pion Bose-Einstein correlations

We report on the high statistics two-pion correlation functions from pp collisions at $\sqrt{s}=0.9$ TeV and $\sqrt{s}$=7 TeV, measured by the ALICE experiment at the Large Hadron Collider. The correlation functions as well as the extracted source radii scale with event multiplicity and pair momentum. When analyzed in the same multiplicity and pair transverse momentum range, the correlation is similar at the two collision energies. A three-dimensional femtoscopic analysis shows an increase of the emission zone with increasing event multiplicity as well as decreasing homogeneity lengths with increasing transverse momentum. The latter trend gets more pronounced as multiplicity increases. This suggests the development of space-momentum correlations, at least for collisions producing a high multiplicity of particles. We consider these trends in the context of previous femtoscopic studies in high-energy hadron and heavy-ion collisions, and discuss possible underlying physics mechanisms. Detailed analysis of the correlation reveals an exponential shape in the outward and longitudinal directions, while the sideward remains a Gaussian. This is interpreted as a result of a significant contribution of strongly decaying resonances to the emission region shape. Significant non-femtoscopic correlations are observed, and are argued to be the consequence of "mini-jet"-like structures extending to low $p_{\rm T}$. They are well reproduced by the Monte-Carlo generators and seen also in $\pi^+\pi^-$ correlations.

A method of η′ decay product selection to detect partial chiral symmetry restoration

In case of chiral U_A(1) symmetry restoration the mass of the eta' boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced. The eta' decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einsten correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results strongly support the mass decrease of the eta' boson. In this paper we propose a method to select pions coming from eta' decays. We investigate the efficiency of the proposed kinematical cut in several collision systems and energies with several simulators. We prove that our method can be used in all investigeted collision systems.

Two-pion Bose–Einstein correlations in Pb–Pb collisions at 2.76 TeV with ALICE

We present the first measurement of pion source radii in Pb–Pb collisions at the Large Hadron Collider. The radii were obtained by analyzing the Bose–Einstein enhancement in two-pion correlation functions. Like at lower energies, the radii drop with increasing transverse momentum, indicating the presence of collective expansion. In absolute terms, all three radii (Rout, Rside, Rlong) are larger than at RHIC, roughly consistent with a linear scaling with the cube root of the particle multiplicity.

Pion femtoscopy inp + pcollisions ats=200GeV

The STAR Collaboration at RHIC has measured two-pion correlation functions from p+p collisions at sqrt(s)=200 GeV. Spatial scales are extracted via a femtoscopic analysis of the correlations, though this analysis is complicated by the presence of strong non-femtoscopic effects. Our results are put into the context of the world dataset of femtoscopy in hadron-hadron collisions. We present the first direct comparison of femtoscopy in p+p and heavy ion collisions, under identical analysis and detector conditions.

Tagging of $ \eta{^\prime}$ decay products to analyze chiral restoration

In case of chiral U_A(1) symmetry restoration the mass of the eta' boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced. The eta' decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einsten correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results strongly support the mass decrease of the eta' boson. In this paper we propose a method to select pions coming from eta' decays. We investigate the efficiency of the proposed kinematical cut in several collision systems and energies with several simulators. We prove that our method can be used in all investigeted collision systems.

An Explanation of a Phenomenon in Relativistic Heavy-Ion Collisions

The multi-source pion interferometry in relativistic heavy-ion collisions is presented and two-source models for hadron gas and hadron gas plus quark-gluon plasma are proposed. The models can resolve the HBT puzzle. For the same q and different direction of q̄, the two-pion correlation functions show characteristic oscillation behaviors, which may be used to distinguish the two-source models. Our research also showes that the multi-source pion correlations can resolve the HBT puzzle.

Effects of source opacity and expansion on two-pion Bose-Einstein correlations

We examine two-pion Bose-Einstein correlations for partially coherent particle-emitting sources within quantum statistical formalism, where the sources are treated as classical currents with chaotic and coherent components. The two-pion correlation functions of the partially coherent sources contain a phase which is sensitive to the asymmetry of the source emission function. We investigate the influence of source opacity and expansion in high energy heavy ion collisions on the phase by Monte Carlo calculations. We find that these two physical effects shift the phase from zero. The Gaussian-formula fit results to the simulated two-pion correlation functions indicate that the opaque and expansion effects lead to a smaller interferometry radius R out and a larger λ parameter.

Two-pion Bose-Einstein correlations inppcollisions ats=900 GeV

We report on the measurement of two-pion correlation functions from pp collisions at $\sqrt{s}=900$ GeV performed by the ALICE experiment at the Large Hadron Collider. Our analysis shows an increase of the HBT radius with increasing event multiplicity, in line with other measurements done in particle- and nuclear collisions. Conversely, the strong decrease of the radius with increasing transverse momentum, as observed at RHIC and at Tevatron, is not manifest in our data.

Characteristic quantities of pion-emitting sources extracted by model-independent analysis in relativistic heavy ion collisions

We examine the characteristic quantities of pion-emitting sources extracted by model-independent imaging analysis in relativistic heavy ion collisions. The moments of the spatial separation of pion pair emission can provide the characteristic information about the source geometry and coherence. They are better for describing the non-Gaussian sources with granular and core-halo structures. An improved granular source model of quark-gluon plasma droplets can reproduce the main characteristics of the two-pion correlation functions and source functions in the experiment of $\sqrt{{s}_{\mathit{NN}}}=200$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions. The transverse-momentum dependence of the normalized first-order moments of the separation for the granular source is consistent with that of the usual interferometry results of source radii, after taking into account the Lorentz contraction in the direction of the transverse momentum of the pion pair.

Detection of source inhomogeneity through event-by-event two-pion Bose–Einstein correlations

We develop a method for detecting the inhomogeneity of the pion-emitting sources produced in ultra-relativistic heavy ion collisions, through event-by-event two-pion Bose–Einstein correlations. The root-mean-square of the error-inverse-weighted fluctuations between the two-pion correlation functions of single and mixed events are useful observables for the detection. By investigating the root-mean-square of the weighted fluctuations for different impact parameter regions people may hopefully determine the inhomogeneity of the particle-emitting in the coming Large Hadron Collider (LHC) heavy ion experiments.