Space-momentum Correlations Research Articles

Spinodal enhancement of fluctuations in nucleus-nucleus collisions

Subensemble Acceptance Method (SAM) [1, 2] is an essential link between measured event-by-event fluctuations and their grand canonical theoretical predictions such as lattice QCD. The method allows quantifying the global conservation law effects in fluctuations. In its basic formulation, SAM requires a sufficiently large system such as created in central nucleus-nucleus collisions and sufficient space-momentum correlations. Directly in the spinodal region of the First Order Phase Transition (FOPT) different approximations should be used that account for finite size effects. Thus, we present the generalization of SAM applicable in both the pure phases, metastable and unstable regions of the phase diagram [3]. Obtained analytic formulas indicate the enhancement of fluctuations due to crossing the spinodal region of FOPT and are tested using molecular dynamics simulations. A rather good agreement is observed. Using transport model calculations with interaction potential we show that the spinodal enhancement of fluctuations survives till the later stages of collision via the memory effect [4]. However, at low collision energies the space-momentum correlation is not strong enough for this signal to be transferred to second and third order cumulants measured in momentum subspace. This result agrees well with recent HADES data on proton number fluctuations at √SNN = 2.4 GeV which are found to be consistent with the binomial momentum space acceptance [5].

Heavy-flavor meson and baryon production in high-energy nucleus-nucleus collisions

We present a new model for the description of heavy-flavor hadronization in relativistic heavy-ion collisions. We explore its effect on the charmed hadron yields and kinematic distributions once the latter is applied at the end of transport calculations used to simulate the propagation of heavy quarks in the deconfined fireball produced in the collision. The model is based on the formation of color-singlet clusters through the recombination of charm quarks with light antiquarks or diquarks from the same fluid cell. This local mechanism of color neutralization leads to a strong space-momentum correlation, which provides a substantial enhancement of charmed baryon production and of the collective flow of all charmed hadrons.

Single-particle space-momentum angle distribution effect on two-pion HBT correlation with Coulomb interaction

We calculate the HBT radius for with Coulomb interaction using the string melting version of a multiphase transport (AMPT) model. We study the relationship between the single-particle space-momentum angle and the particle sources and discuss HBT radii without single-particle space-momentum correlation. Additionally, we study the Coulomb interaction effect on the numerical connection between the single-particle space-momentum angle distribution and the transverse momentum dependence of .

In-medium hadronization of heavy quarks and its effect on charmed meson and baryon distributions in heavy-ion collisions

We present a new model for the description of heavy-quark hadronization in relativistic heavy-ion collisions in the presence of a reservoir of lighter thermal particles with which recombination can occur leading to the formation of color-singlet clusters. Color neutralization is assumed to occur locally, within the same fluid cell occupied by the heavy quark and it proceeds via the recombination of the latter with light antiquarks (quarks) or diquarks (anti-diquarks), which are assumed to be present in the medium with thermal abundance as effective degrees of freedom around the QCD crossover temperature T_c. Typically the resulting color-singlet clusters have quite low invariant mass, in most of the cases below 4 GeV, and in this case they are assumed to undergo an isotropic 2-body decay in their local rest-frame. Heavier clusters are instead fragmented as Lund strings. The possibility of recombination with light diquarks enhances the yields of charmed baryons, in qualitative agreement with recent measurements. The assumption of local color neutralization leads to a strong space-momentum correlation, which provides a substantial enhancement of the collective flow of the final-state charmed hadrons, affecting both their momentum and their angular distributions.

Collectivity of J/ψ Mesons in Heavy-Ion Collisions.

The production of J/ψ mesons in heavy-ion collisions at the Large Hadron Collider is believed to be dominated by the recombination of charm and anticharm quarks in a hot QCD medium. However, measurements of the elliptic flow (v_{2}) of J/ψ mesons in these reactions are not well described by existing calculations of J/ψ recombination for transverse momenta p_{T}≳4 GeV. We revisit these calculations in two main aspects. Employing the resonance recombination model, we implement distribution functions of charm quarks transported through the quark-gluon plasma using state-of-the-art Langevin simulations and account for the space-momentum correlations of the diffusing charm and anticharm quarks in a hydrodynamically expanding fireball. This extends the relevance of the recombination processes to substantially larger momenta than before. We also revisit the suppression of primordially produced J/ψ's by propagating them through the same hydrodynamic medium, leading to a marked increase of their v_{2} over previous estimates. Combining these developments into a calculation of the p_{T}-dependent nuclear modification factor and v_{2} of inclusive J/ψ production in semicentral Pb-Pb collisions at the LHC, we find a good description of the experimental results by the ALICE Collaboration. Our results thus resolve the abovementioned v_{2} puzzle and imply the relevance of recombination processes for p_{T}'s of up to ∼8 GeV.

Implication of two-baryon azimuthal correlations in pp collisions at LHC energies on the QGP

The near-side depression in two-proton or two-antiproton azimuthal correlations in pp collisions at s=7 TeV has been observed experimentally and then qualitatively reproduced in our earlier studies with a multi-phase transport model. In this study, we further investigate the origin of the depression feature in two-baryon correlations in small collision systems. We find that the initial parton-level spatial correlation, a finite expansion in the parton stage, and quark coalescence are important ingredients leading to the near-side depression. In particular, we find that a finite expansion of the parton system leads to a finite space-momentum correlation at hadronization, which then converts the near-side depression in the coordinate space to that in the momentum space. These results suggest that a partonic matter with a finite lifetime is formed in the pp collisions. Further studies are needed to determine whether the partonic matter is near local equilibrium and can thus be called a QGP or far away from local equilibrium.

Understanding the energy dependence of B_2 in heavy ion collisions: interplay of volume and space-momentum correlations

The deuteron coalescence parameter B_2 in proton+proton and nucleus+nucleus collisions in the energy range of sqrt{s_{NN}}= 900–7000 GeV for proton + proton and sqrt{s_{NN}}= 2–2760 GeV for nucleus + nucleus collisions is analyzed with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, supplemented by an event-by-event phase space coalescence model for deuteron and anti-deuteron production. The results are compared to data by the E866, E877, PHENIX, STAR and ALICE experiments. The B_2 values are calculated from the final spectra of protons and deuterons. At lower energies, sqrt{s_{NN}}le 20 GeV, B_2 drops drastically with increasing energy. The calculations confirm that this is due to the increasing freeze-out volume reflected in B_2sim 1/V. At higher energies, sqrt{s_{NN}}ge 20 GeV, B_2 saturates at a constant level. This qualitative change and the vanishing of the volume suppression is shown to be due to the development of strong radial flow with increasing energy. The flow leads to strong space-momentum correlations which counteract the volume effect.

Charm-hadron production in pp and AA collisions

Recent measurements of various charm-hadron ratios in pp, p-Pb and Pb-Pb collisions at the LHC have posed challenges to the theoretical understanding of heavy-quark hadronization. The Λc/D0 ratio in pp and p-Pb collisions shows larger values than those found in e+e− and ep collisions and predicted by Monte-Carlo event generators based on string fragmentation, at both low and intermediate transverse momenta (pT). In AA collisions, the Ds/D ratio is significantly enhanced over its values in pp, while the Λc/D0 data indicates a further enhancement at intermediate pT. Here, we report on our recent developments for a comprehensive description of the charm hadrochemistry and transport in pp and AA collisions. For pp collisions we find that the discrepancy between the Λc/D0 data and model predictions is much reduced by using a statistical hadronization model augmented by a large set of “missing” states in the charm-baryon spectrum, contributing to the Λc via decay feeddown. For AA collisions, we develop a 4-momentum conserving resonance recombination model for charm-baryon formation implemented via event-by-event simulations that account for space-momentum correlations (SMCs) in transported charm- and thermal light-quark distributions. The SMCs, together with the augmented charm-baryon states, are found to play an important role in describing the baryon-to-meson enhancement at intermediate momenta. We emphasize the importance of satisfying the correct (relative) chemical equilibrium limit when computing the charm hadrochemistry and its momentum dependence with coalescence models.

Hadronization and Charm-Hadron Ratios in Heavy-Ion Collisions.

Understanding the hadronization of the quark-gluon plasma (QGP) remains a challenging problem in the study of strong-interaction matter as produced in ultrarelativistic heavy-ion collisions (URHICs). The large mass of heavy quarks renders them excellent tracers of the color neutralization process of the QGP when they convert into various heavy-flavor (HF) hadrons. We develop a 4-momentum conserving recombination model for HF mesons and baryons that recovers the thermal and chemical equilibrium limits and accounts for space-momentum correlations (SMCs) of heavy quarks with partons of the hydrodynamically expanding QGP, thereby resolving a long-standing problem in quark coalescence models. The SMCs enhance the recombination of fast-moving heavy quarks with high-flow thermal quarks in the outer regions of the fireball. We also improve the hadrochemistry with "missing" charm-baryon states, previously found to describe the large Λ_{c}/D^{0} ratio observed in proton-proton collisions. Both SMCs and hadrochemistry, as part of our HF hydro-Langevin-recombination model for the strongly coupled QGP, importantly figure in the description of recent data for the Λ_{c}/D^{0} ratio and D-meson elliptic flow in URHICs.

Light nuclei production in Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ s N N = 2 . 76 TeV

Using the coalescence model based on the phase-space distribution of nucleons from an extended blast-wave model that includes the space-momentum correlation of high momentum nucleons, we study the transverse momentum spectra and elliptic flows of deuteron and helium-3 in Pb+Pb collisions at the energy $\sqrt{s_{NN}}=2.76$ TeV. We find that the measured elliptic flow of deuterons can be satisfactorily described if nucleons of large transverse momenta are assumed to be more spread in space when their momenta are more aligned along the reaction plane.

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.

Scaling of elliptic flow, recombination, and sequential freeze-out of hadrons in heavy-ion collisions

The scaling properties of elliptic flow of hadrons produced in ultrarelativistic heavy-ion collisions are investigated at low transverse momenta, $p_T\lsim 2$\,GeV. Utilizing empirical parameterizations of a thermalized fireball with collective-flow fields, Resonance Recombination Model (RRM) is employed to describe hadronization via quark coalescence at the hadronization transition. We reconfirm that RRM converts equilibrium quark distribution functions into equilibrated hadron spectra including the effects of space-momentum correlations on elliptic flow. This provides the basis for a controlled extraction of quark distributions of the bulk matter at hadronization from spectra of multi-strange hadrons which are believed to decouple close to the critical temperature. The resulting elliptic flow from empirical fits at RHIC exhibits transverse kinetic-energy and valence-quark scaling. Utilizing the well-established concept of sequential freeze-out we find that the scaling at low momenta can be extended to bulk hadrons ($\pi$, $K$, $p$) at thermal freeze-out, and thus result in an overall description compatible with both equilibrium hydrodynamics and quark recombination.

Implications of space–momentum correlations and geometric fluctuations in heavy-ion collisions

The standard picture of heavy-ion collisions includes a collective expansion. If the initial energy density in the collisions is lumpy, then the expansion can convert the spatial lumpiness into correlations between final-state particles. Correlations in heavy-ion collisions show prominent features not present in p+p collisions. I argue that many features of these correlations are related to the transference of over-densities from the initial overlap region into momentum–space during the QGP phase of the expansion. I show results from a toy Monte Carlo model to illustrate the consequences of lumpy initial conditions and a collective expansion.

Space-momentum correlations in 8 AGeV Au+Au collisions

Within the RQMD model, space-momentum correlations, i.e. the correlations between final momentum anisotropy and initial eccentricity, are studied for 8 AGeV Au+Au events classified according to the multi-particle azimuthal correlations. The results show that the final elliptic flow fluctuations depend on the initial collision geometry. There are clear space-momentum correlations for nucleons during the whole dynamical evolution of the collisions.

A Non-Zero Hadronic Elliptic Flow with a Vanished Partonic Elliptic Flow in a Coalescence Scenario

The elliptic flow of a hadron is calculated using a quark coalescence model based on the quark phase space distribution produced by a free streaming locally thermalized quark in a two-dimensional transverse plane at initial time. Without assuming the quark's elliptic flow, it is shown that the hadron obtains a non-zero elliptic flow in this model. The elliptic flow of the hadron is shown to be sensitive to both space momentum correlation and the hadron's internal structure. Quark number scaling is obtained only for some special cases.

Resonance recombination model and quark distribution functions in the quark-gluon plasma

We investigate the consequences of space-momentum correlations in quark phase-space distributions for coalescence processes at the hadronization transition. Thus far it has been proved difficult to reconcile such correlations with the empirically observed constituent quark number scaling (CQNS) at the Relativistic Heavy Ion Collider (RHIC). To address this problem we combine our earlier developed quark recombination model with quark phase-space distributions computed from relativistic Langevin simulations in an expanding quark-gluon plasma (QGP). Hadronization is based on resonance formation within a Boltzmann equation that recovers thermal equilibrium and obeys energy conservation in the quark-coalescence process, while the fireball background is adjusted to hydrodynamic simulations of semicentral $\mathrm{Au}\text{\ensuremath{-}}\mathrm{Au}$ collisions at RHIC. To facilitate the applicability of the Langevin process, we focus on strange and charm quarks. Their interactions in the QGP are modeled using leading-order perturbative QCD augmented by effective Lagrangians with resonances that smoothly merge into hadronic states formed at ${T}_{c}$. The interaction strength is adjusted to reproduce the empirical saturation value for the quark-elliptic flow, ${v}_{2,q}^{\mathrm{sat}}\ensuremath{\simeq}7\text{\ensuremath{-}}8%$. The resulting \ensuremath{\phi} and $J/\ensuremath{\psi}$ elliptic flow recover CQNS over a large range in transverse momentum (${p}_{T}$) within a few percent. As a function of transverse kinetic energy, both the quark spectra from the Langevin simulations and the meson spectra generated via resonance recombination recover CQNS from zero to at least $3 \mathrm{GeV}$.

Multi-particle azimuthal correlations and elliptic flow fluctuations in 2A GeV Au+Au collisions

Multi-particle azimuthal correlations between different anisotropic flow and elliptic flow fluctuations are investigated in 2A GeV Au+Au collisions within the RQMD model. The results show that the difference of elliptic flow in different events are developed in the early stage of reactions, and there exist strong space–momentum correlations for nucleons during the collective expansion of system. The fluctuations in the initial collision geometry and dynamical evolution of heavy ion collisions are not negligible.

Phase-space coalescence for heavy and light quarks at RHIC

We review the application and successes of a phase-space coalescence plus fragmentation model that has been applied for hadronization at RHIC. The physical concept is discussed together with the practical implementation. The robustness of main predictions is reviewed together with several open issues like relevance of three dimensional calculation, finite width of the wave functions, effects of quark masses, energy-entropy conservation, space-momentum correlation. Eventually the relevance of coalescence also for the study of the microscopic interaction of heavy quarks is highlighted.

Space-time characterization and collective motion at intermediate energies

Shape analyses of two-particle correlation functions are discussed. Two-proton imaging provides information about the volume, the relative contributions between fast and slow emitting sources and the profile of the two-particle source that can be directly compared to microscopic model simulations. In the case of correlations between complex particles, the role played by collective motion and space-momentum correlations needs special considerations. By means of a semi-quantitative Monte Carlo approach, deuteron-alpha correlation functions measured in Xe+Au collisions at E/A=50 MeV are investigated. The comparison reveals the existence of a position-relative momentum correlation that reduces the apparent source size and distorts the line-shape of the correlation function. The developed ideas show how intensity interferometry with complex particles is sensitive not only to the geometry of the system but also to the interplay between collective and thermal motion.

TWO-PARTICLE CORRELATION IN HEAVY-ION COLLISIONS AT CSR ENERGY

The predictions of the two-particle correlation by using the relativistic quantum molecular dynamics model are presented for the heavy-ion reactions at HIRFL-CSR energy. The two-proton correlation function with the final state interaction is calculated with the Lednicky code for the U + U collisions at beam energy 520 A MeV. Applying the imaging technique, the relationship between the freeze-out spatial distributions and the results of correlation femtoscopy is investigated. We find that one can reliably reconstruct the source functions from the two-particle correlation functions with ignoring the degree of space-momentum correlations at this energy. The results are useful to the designing the hadron detector at CSR.