Phase-Space Coalescence for heavy and light quarks at RHIC
V. Greco
备注：
Talk given at the Zimanyi 75 Memorial Workshop on "Hadronic and Quark Matter", Budapest, July 2-4, 2007. To appear in The European Physical Journal (Special Topics)
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.
A new dynamical approach that combines covariant parton transport theory with hadronization channels via parton coalescence and fragmentation is applied to Au+Au at RHIC. Basic consequences of the simple coalescence formulas, such as elliptic flow scaling and enhanced proton/pion ratio, turn out to be rather sensitive to the spacetime aspects of coalescence dynamics.
Quark coalescence models have been applied successfully to reproduce measured hadron production data in relativistic heavy ion collisions at SPS and RHIC energies, which finding strongly supports the formation of deconfined quark matter in these collisions. The investigation of meson and baryon production is an ideal tool to understand dynamical details of hadronization, especially strange hadron numbers and ratios. We display latest results on the production of strange particles in quark coalescence processes in heavy ion collisions at different collider energies.
Transverse momentum spectra of pions, protons and antiprotons in Au+Au collisions at intermediate RHIC energy of $\sqrt{s_{NN}}=62$ GeV are studied in a model that includes both quark coalescence from the dense partonic matter and fragmentation of the quenched perturbative minijet partons. The resulting baryon to meson ratio at intermediate transverse momenta is predicted to be larger than that seen in experiments at higher center of mass energies.
Recent experimental data support the presence of quark coalescence in heavy ion collisions at RHIC energies. Hadronization of quark matter and hadron formation in heavy ion collisions can be described by the coalescence process, and measured data are reproduced successfully. On the other hand, the theoretical coalescence calculations are based on a non-relativistic description. Here we investigate the robustness of the coalescence description, using different wave-function overlap during hadron formation.
From covariant transport theory, a significant ~10% light quark elliptic flow at RHIC implies an elliptic flow of similar magnitude for charm quarks, at moderately large pT > 2.5 - 3 GeV. At lower transverse momenta, charm quark elliptic flow reduces progressively, reminiscent of the mass ordering pattern in ideal hydrodynamics. From the quark flows we predict the elliptic flow of D mesons at RHIC via quark coalescence. The large parton opacities needed to generate the light quark flow also lead to substantial ~40-50% secondary charm production.
Coalescence of minijet partons with the partons from the quark-gluon plasma formed in relativistic heavy ion collisions is suggested as the mechanism for production of hadrons with intermediate transverse momentum. The resulting enhanced antiproton and pion yields at intermediate transverse momentum gives a plausible explanation for the observed large antiproton to pion ratio. With further increasing momentum, the ratio is predicted to decrease and approach the small value given by independent fragmentations of minijet partons after their energy loss in the quark-gluon plasma.
We investigate the coalescence factors $B_2$ and $B_3$ at low collision energies ($\sqrt{s_\mathrm{NN}}<6$ GeV) with special focus on the HADES and RHIC-BES experiments. It is shown that, in order to properly interpret the coalescence factors $B_A$, two important corrections are necessary: I) $B_2$ has to be calculated using the proton $\times$ neutron yields in the denominator, instead of the square of the proton yield, and II) the primordial proton (neutron) densities have to be used for the normalization and not the final state (free) protons (neutrons). Both effects lead to a drastic reduc…
The influence of spacetime dynamics in hadronization via parton coalescence at RHIC is investigated using covariant parton transport theory. Key observables, the quark number scaling of elliptic flow and the enhancement of the p/pi ratio, show strong dynamical effects and differ from earlier results based on the simple coalescence formulas.
Using a covariant coalescence model, we study hadron production in relativistic heavy ion collisions from both soft partons in the quark-gluon plasma and hard partons in minijets. Including transverse flow of soft partons and independent fragmentation of minijet partons, the model is able to describe available experimental data on pion, kaon, and antiproton spectra. The resulting antiproton to pion ratio is seen to increase at low transverse momenta and reaches a value of about one at intermediate transverse momenta, as observed in experimental data at RHIC. A similar dependence of the antikao…
The production rate of negative parity baryons was found to be much weaker than that of positive states in RHIC experiments. In the present paper we show that this suppression is a simple consequence of the coalescence dynamics of hadronization.
We study (anti)deuteron formation rates in heavy-ion collisions in the framework of a wave-function based coalescence model. The main feature of our model is that nucleons are emitted from the whole spherically symmetric fireball volume, while antinucleons are emitted only from a spherical shell close to the surface. In this way, the model accounts for nucleon-antinucleon annihilations in the center of the reaction at lower beam energies. Comparison with experimental data on the coalescence parameter in the range $\sqrt{s_{NN}}= 4.7-200$ GeV allows us to extract radii of the respective source …
Based on the quark coalescence model, we derive relations among the momentum anisotropies of mesons and baryons in relativistic heavy ion collisions from a given, but arbitrary azimuthal distribution for the partons. Besides the familiar even Fourier coefficients such as the elliptic flow, we also pay attention to odd Fourier coefficients such as the directed flow, which has been observed at finite rapidity even at RHIC energies.
We show that either mass ordering or quark number scaling of anisotropic flow can result from quark coalescence, depending on the nature of phase space correlations at hadronization. Quark number scaling signals nonequilibrium dynamics because it can only appear when hydrodynamic correlations break down. However, the scaling does not hold for all nonthermal distributions, and is compatible with covariant transport theory only if remarkable cancellations occur at RHIC.
A study of elliptic flow of open charm mesons, $D^0$ and $D_S ^\pm$ using quark coalescence as a mechanism of hadronization of heavy quarks implemented in conjunction with A Multi Phase Transport (AMPT) model has been presented. We have studied the transverse momentum dependence of the elliptic flow parameter at mid-rapidity ($|y|$ $<$ 1.0) for Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV (RHIC) and Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV (LHC) for different values of partonic interaction cross-section and QCD coupling constant. We have compared our calculations with the experimentally…
We review hadron formation from a deconfined quark gluon plasma (QGP) via coalescence or recombination of quarks and gluons. We discuss the abundant experimental evidence for coalescence from the Relativistic Heavy Ion Collider (RHIC) and compare the various coalescence models advocated in the literature. We comment on the underlying assumptions and remaining challenges as well as the merits of the models. We conclude with a discussion of some recent developments in the field.
We study the production of charm mesons and other charm baryons from quark matter at CERN SPS and RHIC energies. Using quark coalescence models as hadronization mechanism, we predict particle ratios, absolute yields and transverse momentum spectra.
In a coalescence plus independent fragmentation approach we calculate the $p_T$ spectra of the main hadrons: $π, K, p, \bar p, Λ, ϕ$ in a wide range of transverse momentum from low $p_T$ up to about 10 GeV. The approach in its main features was developed several years ago at RHIC energy. Augmenting the model with the inclusion of some more main resonance decays, we show that the approach correctly predicts the evolution of the $p_T$ spectra from RHIC to LHC energy and in particular the baryon-to-meson ratios $p/π,\bar p/π,Λ/K$ that reach a value of the order of unit at $p_T \sim 3\, \rm GeV$. …
With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be…
This thesis discusses the phenomenological parton recombination approach to describe hadronization in heavy ion collisions. The very good agreement to RHIC data for the flow coefficients v_2 and v_4 is shown and extrapolations are used to make predictions for the LHC.
The production of heavy clusters in nuclear reactions is important in a wide variety of applications: radiation shielding, space engineering and design, medical physics, accelerator design, and more. According to the Cascade Exciton Model (CEM), there are three ways high-energy heavy clusters can be produced. The first way is via coalescence of nucleons produced in the IntraNuclear Cascade (INC). The second way is via the preequilibrium model. The last way is via Fermi breakup. Previous work in CEM examines the impact of expansions of the preequilibrium model and Fermi breakup model on heavy c…
The current status of the application of hydrodynamics to ultrarelativistic heavy ion collisions is reviewed. We elaborate on the arguments for strong transverse flow and rapid thermalization and discuss future applications and trends in hydrodynamics.
To study heavy ion collisions at energies to be available from the Relativistic Heavy Ion Collider (RHIC), we have developed a transport model that includes both initial partonic and final hadronic interactions. Specifically, the parton cascade model ZPC, which uses as input the parton distribution from the HIJING model, is extended to include the quark-gluon to hadronic matter transition and also final-state hadronic interactions based on the ART model. Comparisons with SPS data and predictions for RHIC are reported.
The relativistic hydrodynamics together with the single-freeze-out statistical hadronization model is used to describe the midrapidity hadron production in ultra-relativistic heavy-ion collisions at RHIC and LHC. At the highest RHIC energy our approach gives a quite satisfactory global description of soft hadronic observables including the HBT radii. With the increased initial energy, from RHIC to LHC, we expect the saturation of the pion elliptic flow and the moderate increase of the correlation radii.
Effects of partonic interactions in heavy ion collisions at RHIC are studied in a multiphase transport model (AMPT) that includes both initial partonic and final hadronic interactions.It is found that a large parton scattering cross section is needed to understand the measured elliptic flow of pions and two-pion correlation function.
We calculate the contribution of the two photon production process into $e^+e^-$ spectra, and compare the results with experimental data from the PHENIX detector at RHIC. We study the contribution given by ``semi-coherent" kinematics, in which one photon is relatively hard and is incoherently emitted by participating protons, while another can be soft enough to be in a coherent domain.
Current status of dynamical modeling of relativistic heavy ion collisions and hydrodynamic description of the quark gluon plasma is reported. We find the hadronic rescattering effect plays an important role in interpretation of mass splitting pattern in the differential elliptic flow data observed at RHIC. To demonstrate this, we predict the elliptic flow parameter for phi mesons to directly observe the flow just after hadronisation. We also discuss recent applications of outputs from hydrodynamic calculations to J/psi suppression, thermal photon radiation and heavy quark diffusion.
There are several indications that an opaque partonic medium is created in energetic Au+Au collisions \sqrt{s} ~ 100 GeV/nucleon at the Relativistic Heavy Ion Collider (RHIC). At the extreme densities of ~ 10-100 times normal nuclear density reached even heavy-flavor hadrons are affected significantly. Heavy-quark observables are presented from the parton transport model MPC, focusing on the nuclear suppression pattern, azimuthal anisotropy ("elliptic flow"), and azimuthal correlations. Comparison with Au+Au data at top RHIC energy \sqrt{s} = 200 GeV indicates significant heavy quark rescatter…
We show that hadronization via quark coalescence enhances hadron elliptic flow at large pT relative to that of partons at the same transverse momentum. Therefore, compared to earlier results based on covariant parton transport theory, more moderate initial parton densities dN/dη(b=0) ~ 1500-3000 can explain the differential elliptic flow v_2(pT) data for Au+Au reactions at s^1/2=130 and 200 AGeV from RHIC. In addition, v2(pT) could saturate at about 50% higher values for baryons than for mesons. If strange quarks have weaker flow than light quarks, hadron v_2 at high pT decreases with relative…
Both dilepton and charm production at RHIC are considered to be important signatures for Quark-Gluon Plasma production. Recently it was argued by S.Gavin, P.L.McGaughey,P.V. Ruuskanen and R.Vogt that the background from semileptonic correlated charm decays is so large that it makes dilepton measurements virtually impossible. We show that this conclusion in fact is in fact reversed if the energy loss due to secondary interaction of charmed quarks is included.
With the adiabatic assumption in the cooling process, we discussed a new mechanism on Upsilon(1S) suppression that is due to the fast heating process at the early stage of the fireball instead of its finite decay width in finite temperature medium produced in the heavy ion collisions. We calculated the transition probability after the fast heating dissociation as a function of the temperature of the medium and the nuclear modification factor in central collisions, and found that the suppression is not negligible at RHIC, even if the width of Upsilon(1S) vanishes.
A status report on the jet quenching physics in heavy-ion collisions is given as it appears after more than 10 years of collecting and analysing data at the Relativistic Heavy Ion Collider (RHIC) and ~1.5 years of physics at the Large Hadron Collider (LHC). The (theoretical) predictions and expectations before the start of the LHC program are contrasted with the most recent experimental results, focussing on the nuclear modification factor R_{AA}, the elliptic flow v_2 of high-p_T particles, and on the problem of initial conditions.
We describe ultra-relativistic heavy ion collisions at RHIC and the LHC with a hybrid model using the IP-Glasma model for the earliest stage and viscous hydrodynamics and microscopic transport for the later stages of the collision. We demonstrate that within this framework the bulk viscosity of the plasma plays an important role in describing the experimentally observed radial flow and azimuthal anisotropy simultaneously. We further investigate the dependence of observables on the temperature below which we employ the microscopic transport description.
We systematically investigate the pion transverse momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss (HBT) interferometry in the granular source model for the heavy ion collisions of Au-Au at $\sqrt{s_{NN}}=$ 200 GeV and Pb-Pb at $\sqrt{s_{NN}}=$ 2.76 TeV with different centralities. The granular source model can well reproduce the experimental results of the heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). We examine the parameters involved in the granular source model. The experimental data of the momentum spectrum, elliptic flow,…
The large and saturating differential elliptic flow v2(pT) observed in Au+Au reactions at RHIC so far could only be explained assuming an order of magnitude denser initial parton system than estimated from perturbative QCD. Hadronization via parton coalescence can resolve this ``opacity puzzle'' because it enhances hadron elliptic flow at large pT relative to that of partons at the same transverse momentum. An experimentally testable consequence of the coalescence scenario is that v2(pT) saturates at about 50% higher values for baryons than for mesons. In addition, if strange quarks have weake…
Perturbative QCD results on pion production are presented in proton-proton, proton-nucleus and nucleus-nucleus collisions from CERN SPS up to RHIC energy. A K_{jet}(s, p_T, Q) factor obtained from jet production is applied to perform next-to-leading order calculations. Using the intrinsic transverse momentum (k_T) we determined transverse momentum spectra for pions in wide energy region. We have investigated nuclear multiscattering and the Cronin effect at RHIC energies.
Maurice Jacob played a key role in bringing together different groups from the experimental and theoretical nuclear and particle physics communities to initiate an ultrarelativistic heavy-ion collision program at the CERN SPS, in order to search for the quark-gluon plasma. I review the history of this program from its beginnings to the time when the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) started operation. I close by providing a glimpse of the important discoveries made at RHIC and giving an outlook towards heavy-ion collisions at the Large Hadron Collid…
J/psi production and collective flow is studied with a coalescence model based on phase space distribution of charm quarks from a multi-phase transport model simulation of relativistic heavy ion collisions. Both the yield and the flow of J/psi particles are sensitive to charm quark final state interactions. As the charm quark rescattering cross section increases from 3 mb to 10 mb, J/psi elliptic flow increases faster than corresponding light hadron elliptic flows. The v_2(p_t) of J/psi crosses that of D mesons to reach a value that is about the peak value of the D meson flow but at a higher p…
We show that a consistent hydrodynamic description of soft-hadronic one- and two-particle observables (the HBT radii) studied in the relativistic heavy-ion collisions at RHIC may be obtained if one uses the Gaussian energy density profile as the initial condition. The transverse-momentum spectra, the elliptic flow coefficient $v_2$, and the pionic azimuthally sensitive HBT radii are successfully reproduced, which hints that the long standing HBT puzzle has been solved.
We present predictions for the formation of (anti)nuclear bound states in Au+Au central collisions at $\sqrt{s}=200A$ GeV. The coalescence afterburner was applied to the freeze-out phase space distributions of nucleons provided by the transport model, RQMD version 2.4. We study the sensitivity of the deuteron spectra to space-momentum correlations. It is found that the deuteron transverse momentum distributions are strongly affected by the nucleon space-momentum correlations.
Using a multiphase transport model (AMPT) with both partonic and hadronic interactions, we study the multiplicity and transverse momentum distributions of charged particles such as pions, kaons and protons in central Au+Au collisions at RHIC energies. Effects due to nuclear shadowing and jet quenching on these observables are also studied. We further show preliminary results on the production of multistrange baryons from the strangeness-exchange reactions during the hadronic stage of heavy ion collisions.
Heavy ion collisions at extremely high energy, such as the top energy at RHIC, exhibit the property of transparency where there is a clear separation between the almost net-baryon-free central rapidity region and the net-baryon-rich fragmentation region. We calculate the net-baryon rapidity loss and the nuclear excitation energy using the energy-momentum tensor obtained from the McLerran-Venugopalan model. Nuclear compression during the collision is further estimated using a simple space-time picture. The results show that extremely high baryon densities, about twenty times larger than the nor…
The direct photon spectrum measured by the PHENIX collaboration in Au + Au collisions at sqrt{s_{NN}}=200 GeV has been analyzed. It has been shown that the data can be reproduced reasonably well by assuming a deconfined state of thermalized quarks and gluons. The effects of the equation of state on the value of the initial temperature have been studied. The modifications of hadronic properties at non-zero temperature have been taken in to account.
The implications of parton rearrangement processes on the dynamics of ultra-relativistic heavy-ion collisions have been investigated. A microscopic transport approach, namely the quark gluon string model (QGSM) which has been extended for a locally density-dependent partonic rearrangement and fusion procedure served as the tool for this investigations. The model emulates effectively the dynamics of a strongly coupled quark plasma and final hadronic interactions. Main QGSM results on anisotropic flow components v1 and v2 at top RHIC energy are compiled. Predictions for the pseudorapidity depend…
In this talk we present a perturbative QCD improved parton model calculation for light meson production in high energy heavy ion collisions. In order to describe the experimental data properly, one needs to augment the standard pQCD model by the transverse momentum distribution of partons ("intrinsic k_T"). Proton-nucleus data indicate the presence of nuclear shadowing and multiscattering effects. Further corrections are needed in nucleus-nucleus collisions to explain the observed reduction of the cross section. We introduce the idea of proton dissociation and compare our calculations with the…
We give a theoretical overview of the heavy quark tomography puzzle posed by recent non-photonic single electron data from central Au+Au collisions at $\sqrt{s} = 200$ AGeV. We show that radiative energy loss mechanisms alone are not able to explain large single electron suppression data, as long as realistic parameter values are assumed. We argue that combined collisional and radiative pQCD approach can solve a substantial part of the non-photonic single electron puzzle.
Upsilon production in heavy ion collisions at RHIC energy is investigated. While the transverse momentum spectra of the ground state Upsilon(1s) are controlled by the initial state Cronin effect, the excited $b\bar b$ states are characterized by the competition between the cold and hot nuclear matter effects and sensitive to the dissociation temperatures determined by the heavy quark potential. We emphasize that it is necessary to measure the excited heavy quark states in order to extract the early stage information in high energy nuclear collisions at RHIC.
We argue that measurements of identified-particle elliptic flow in a wide energy range could shed light on the possible phase change in high-energy heavy ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC). When the hadronization process is dominated by quark coalescence, the number-of-constituent-quark (NCQ) scaling for the identified-particle elliptic flow can serve as a probe for studying the strong interacting partonic matter. In the upcoming RHIC low-energy runs, the NCQ scaling behavior may be broken because of the change of the effective degrees of freedom of the hot dense …
I review the latest heavy flavor measurements at RHIC experiments. Measurements from RHIC together with preliminary results from LHC offer us an opportunity to systematically study the sQGP medium properties. In the end, I will outlook a prospective future on precision heavy flavor measurements with detector upgrades at RHIC.
Heavy quark coalescence probability in the presence of a potential
GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心有限公司）；Institute for Theoretical Physics, Johann Wolfgang Goethe Universität, Frankfurt am Main（法兰克福约翰·沃尔夫冈·歌德大学理论物理研究所）；Helmholtz Research Academy Hessen for FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）
Open charm production and $Λ_{c}^{+}/D^{0}$ ratio in pp and Au+Au collisions at the RHIC
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室和粒子物理研究所）；School of Physics and Mechanics, Wuhan University of Technology（武汉理工大学物理与机电工程学院）；School of Mathematics and Physics, China University of Geosciences (Wuhan)（中国地质大学（武汉）数学与物理学院）
The coalescence model assumes instant formation of a bound state from unbound particles based on the overlapping of two states in spatial and momentum spaces and quantum numbers. Therefore, applied to the hadronization of partons, it provides a snapshot of a Quark-Gluon Plasma (QGP) just before hadronization. We use the coalescence model for the formation of the ground state of open heavy flavor and the statistical model for heavier states. Assuming that all heavy flavors in thermal equilibrium hadronize through the coalescence, we find that the QGP just before hadronization is not composed of…
At the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, heavy nuclei are collided at high energies to create matter that is hot enough and dense enough to dissolve hadrons into a quark-gluon-plasma (QGP). In this lecture, dedicated to the memory of Aditya Sambamurti, I present an introduction to heavy-ion collisions and highlights from the first decade of RHIC results.
Heavy quarks are initially produced in nuclear collisions and the number is conserved during the evolution of the system. We establish a sequential coalescence model with charm conservation and apply it to charmed hadron production at RHIC and LHC energies. The charm conservation enhances the earlier formed hadrons and reduces the later formed ones, which leads to a $D_s/D^0$ enhancement and a $Λ_c/D^0$ suppression. The mass dependence of the sequential hadron formation provides us a new tool for studying the quark-gluon plasma hadronization in high energy nuclear collisions.
In this article, we briefly review recent progress on hydrodynamic modeling and its implementations to relativistic heavy-ion collisions at RHIC and the LHC. The related topics include: 1) initial state fluctuations, final state correlations and event-by-event hydrodynamics, 2) extracting the QGP shear viscosity from flow data, 3) flow and hydrodynamics in 5.02 A TeV p+Pb collisions.
Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.
