Negative Elliptic Flow of $J/ψ$'s: A Qualitative Signature for Charm Collectivity at RHIC
Daniel Krieg, Marcus Bleicher
备注：
4 pages, 3 figures; to be published in EPJ A; Changes: Added B-meson elliptic flow and data on non-photonic electron v_2 to Fig. 2; Added a plot showing the quark v_2; Added discussion about D^0 flow
We discuss one of the most prominent features of the very recent preliminary elliptic flow data of $J/Ψ$ meson from the PHENIX collaboration \cite{Silvestre:2008tw}. Even within the the rather large error bars of the measured data a negative elliptic flow parameter ($v_2$) for $J/Ψ$ in the range of $p_T=0.5-2.5 \GeV/c$ is visible. We argue that this negative elliptic flow at intermediate $p_T$ is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus-nucleus reactions at RHIC. Within a parton recombination approach we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks. The numerical value of the transverse flow velocity $β_T$ for charm quarks that is necessary to reproduce the data is $β_T(charm)\sim 0.55-0.6c$ and therefore compatible with the flow of light quarks.
Based on A Multi-Phase Transport model, the elliptic flow $v_{2}$ of $ϕ$ mesons which is reconstructed from $K^{+}K^{-}$ at the Relativistic Heavy Ion Collider (RHIC) energy has been studied. The results show that reconstructed $v_{2}$ of $ϕ$ meson can keep the earlier information before $ϕ$ decays and it seems to obey the number of constituent quark scaling as other mesons and baryons. This result indicates that the $ϕ$ $v_2$ mostly reflects the parton level collectivity developed during the early stage of the collisions and the strange and light up/down quarks have similar collectivity prope…
New results on $ϕ$-meson production and elliptic flow $v_{2}$ measurements from RHIC 2004 run (Run-IV) have been reviewed. In addition, the di-hadron correlation function between the trigged $ϕ$ and $Ω$ and the associated soft particles was simulated. Knowledge about these results are discussed.
Based on A Multi-Phase Transport (AMPT) model, we have studied the elliptic flow $v_{2}$ of $ϕ$ mesons from reconstructed $K^{+}K^{-}$ decay channel at the top Relativistic Heavy Ion Collider energy at Brookhaven National Laboratory. The dependences of $v_{2}$ on transverse momentum $p_T$ and collision centrality are presented and the rescattering effect of $ϕ$ mesons in the hadronic phase is also investigated. The results show that experimental measurement of $v_{2}$ for $ϕ$ mesons can retain the early collision information before $ϕ$ decays and that the $ϕ$ $v_2$ value obeys the constituent …
We study the production of charmonia and charmed hadrons for nucleus-nucleus collisions at SPS, RHIC, and LHC energies within the framework of the statistical hadronization model. Results from this model are compared to the observed centrality dependence of J/psi production at SPS energy. We further provide predictions for the centrality dependence of the production of open and hidden charm mesons at RHIC and LHC.
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.
Using the perturbative method for the simulation of charmed particles, the dynamical origin of charm quark elliptic flow is studied in the framework of a multi-phase transport (AMPT) model. Besides the expected ordering relative to that of light quarks according to quark masses, charm quark elliptic flow is seen to be sensitive to the parton scattering cross section. To describe the observed large elliptic flow of electrons from the decay of charmed mesons, a charm quark elastic scattering cross section much larger than that estimated from the perturbative QCD is required.
Charm elliptic flow in heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) is studied in a multiphase transport model. Assuming that the cross section for charm quark scattering with other light quarks is the same as that between light quarks, we find that both charm and light quark elliptic flows are sensitive to the value of the cross section. Compared to that of light quarks, the elliptic flow of charm quarks is smaller at low transverse momentum but approaches comparable values at high transverse momentum. Similar features are seen in the elliptic flow of charmed mesons as w…
We report a first attempt (i) to derive constraints on the energy loss of charm quarks in a deconfined medium from the recent PHENIX data of single-electron transverse momentum spectra and (ii) to estimate the resulting suppression of dileptons from correlated semi-leptonic decays of open charmed mesons. The momentum imbalance of photon-tagged light-quark jets is also considered.
We calculate transverse-momentum ($p_t$) spectra and elliptic flow of $J/ψ$'s in $Au$-$Au$ and $Cu$-$Cu$ collisions at RHIC. We employ an earlier constructed 2-component approach for direct and regenerated charmonia which is fairly consistent with the centrality dependence of inclusive $J/ψ$ yields at SPS and RHIC. Discrepancies with high-$p_t$ data in $Cu$-$Cu$ collisions are addressed by implementing effects of a finite formation time and an estimate of $B$ meson feeddown, which largely resolve the problem. The sensitivity of the spectra to the Cronin effect and different in-medium dissociat…
Experimental measurements in collisions of small systems from p+p to p/d/3He+A at RHIC and the LHC reveal particle emission patterns that are strikingly similar to those observed in A+A collisions. One explanation of these patterns is the formation of small droplets of quark-gluon plasma followed by hydrodynamic evolution. A geometry engineering program was proposed [1] to investigate these emission patterns, and the experimental data from that program in p+Au, d+Au, 3He+Au collisions for elliptic and triangular anisotropy coefficients v2 and v3 follow the pattern predicted by hydrodynamic cal…
Heavy quark energy loss in a hot QCD plasma is computed taking into account the competing effects due to suppression of zeroth order gluon radiation below the plasma frequency and the enhancement of gluon radiation due to first order medium induced Bremsstrahlung. The results suggest a surprising degree of cancellation between the two medium effects for charm quarks and provides a possible explanation for the null effect observed by PHENIX in the prompt electron spectrum in Au+Au at $\surd s=$ 130 AGeV.
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.
Recent PHENIX Au+Au -> e- + X data from open charm decay are shown to be consistent with two extreme opposite dynamical scenarios of ultra-relativistic nuclear reactions. Perturbative QCD without final state interactions was previously shown to be consistent with the data. However, we show that the data are also consistent with zero mean free path hydrodynamics characterized by a common transverse flow velocity field. The surprising coincidence of both D and B hydrodynamic flow spectra with pQCD up to p_T ~ 3 and 5 GeV, respectively, suggests that heavy quarks may be produced essentially at re…
We study the production of charmonia and charmed hadrons in nucleus-nucleus collisions at SPS, RHIC, and LHC energies within the framework of the statistical hadronization model. Results from this model are compared to the measured yields and centrality dependence of J/psi production at SPS and RHIC energies. We explore and contrast the centrality dependence of the production of mesons with open and hidden charm at SPS, RHIC, and LHC. The sensitivity of the results to various input parameters is analyzed in detail for RHIC energy.
We study $b\bar{b}$ and $c\bar{c}$ production and the influence of nuclear shadowing at LHC and RHIC energies. We find a significant reduction in the production cross section of both charm and bottom at RHIC and LHC. Bound states such as $Υ$ and $J/Ψ$ are suppressed by this reduction in the charm production cross sections. Therefore, $J/Ψ$ suppression may not be useful as a signature for the quark gluon plasma.
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.
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 anti-charm 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\geq$4 GeV. Here, we revisit these calculations in two main aspects. By employing the resonance recombination model, we implement distribution functions of charm quarks transported through the quark-gluon plasma using state-of-the-…
We review the collectivity and the suppression pattern of charmed mesons - produced in proton-nucleus and nucleus-nucleus collisions at SPS (158 AGeV) and RHIC energies (21 ATeV) - in comparison to dynamical and thermal models. In particular, we examine the charmonium `melting' and the `comover dissociation' scenarios - implemented in a microscopic transport approach - in comparison to the available data from the SPS and RHIC. The analysis shows that the dynamics of c, c-bar quarks at RHIC are dominated by partonic or `pre-hadronic' interactions in the strongly coupled plasma stage. Both the `…
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We present results on rapidity and transverse momentum distributions of inclusive charm quark production in heavy-ion collisions at RHIC, including the next-to-leading order, $O(α_s^3)$, radiative corrections and the nuclear shadowing effect. We find the effective, nuclear K-factor to be $K(y)\approx 1.4$ for $\mid y\mid \leq 3$ in the rapidity distribution, while $1\leq K(p_{T}) \leq 3$ for $1GeV\leq p_T \leq 6GeV$ in the $p_T$ distribution. We incorporate multiple parton scatterings in our calculation of the fraction of all central events that contain at least one charm quark pair. We obtain…
We make up-to-date QCD predictions for open charm and bottom production at RHIC in nucleon-nucleon collisions at \sqrt{S} = 200 GeV. We also calculate the electron spectrum resulting from heavy flavor decays to allow direct comparison to the data. A rigorous benchmark, including the theoretical uncertainties, is established against which nuclear collision data can be compared to obtain evidence for nuclear effects.
Quantum Chromodynamics (QCD) is a basic gauge field theory to describe strong interactions. Lattice QCD calculations predict a phase transition from hadronic matter to a deconfined, locally thermalized Quark-Gluon Plasma (QGP) state at high temperature and small baryon density. Plenty of exciting results from RHIC experiments in the first three years have demonstrated that a hot dense matter with strong collective motion which cannot be described with hadronic degrees of freedom was created at RHIC. Charm quarks are believed to be mostly created from initial gluon fusion in heavy ion collision…
The production of charmonia is investigated for heavy-ion collisions from SPS to RHIC energies. Our approach incorporates two sources of $J/Ψ$ yield: (i) a direct contribution arising from early (hard) parton-parton collisions, subject to subsequent nuclear absorption, quark-gluon plasma and hadronic dissociation, and (ii) statistical production at the hadronization transition by coalescence of $c$ and $\bar{c}$ quarks. Within an expanding thermal fireball framework, the model reproduces $J/Ψ$ centrality dependencies observed at the SPS in Pb-Pb and S-U collisions reasonably well. The study of…
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The production and space-time evolution of charm and bottom quarks in nucleus-nucleus collisions at RHIC and LHC are investigated with the partonic transport model BAMPS (Boltzmann Approach of MultiParton Scatterings). Heavy quarks, produced in primary hard parton scatterings during nucleon-nucleon collisions, are sampled using the Monte Carlo event generator PYTHIA or the leading order mini-jet model in conjunction with the Glauber model, revealing a strong sensitivity on the parton distribution functions, scales, and heavy quark mass. In a comprehensive study exploring different charm masses…
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…
Important goals of RHIC and LHC experiments with ion beams include the creation and study of new forms of matter, such as the Quark Gluon Plasma. Heavy quark production and attenuation will provide unique tomographic probes of that matter. We predict the suppression pattern of open charm and beauty in $Au+Au$ collisions at RHIC and LHC energies based on the DGLV formalism of radiative energy loss. A cancelation between effects due to the $\sqrt{s}$ energy dependence of the high $p_T$ slope and heavy quark energy loss is predicted to lead to surprising similarity of heavy quark suppression at R…
The complete understanding of the basic constituents of hadrons and the hadronic dynamics at high energies are two of the main challenges for the theory of strong interactions. In particular, the existence of intrinsic heavy quark components in the hadron wave function must be confirmed (or disproved). In this paper we propose a new mechanism for the production of $D$-mesons at forward rapidities based on the Color Glass Condensate (CGC) formalism and demonstrate that the resulting transverse momentum spectra are strongly dependent on the behavior of the charm distribution at large Bjorken $x$…
Qualitative features of multiparticle correlations in light-heavy ion ($p+A$) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include i) the ordering of the magnitudes of the azimuthal angle $n$th Fourier harmonics of two-particle correlations $v_n\{2\}$, ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic $v_2\{4\}$, and iii) the energy dependence of four-particle symmetric cumulants measuring correlations bet…
We assess the theoretical uncertainties on the inclusive J/psi production cross section in the Color Evaporation Model (CEM) using values for the charm quark mass, renormalization and factorization scales obtained from a fit to the charm production data. We use our new results to provide improved baseline comparison calculations at RHIC and the LHC. We also study cold matter effects on J/psi production at leading relative to next-to-leading order in the CEM within this approach.
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We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Non-perturbative interaction between heavy quarks and light quarks have been taken into account through a quasi-particle approach in which light partons are dressed with thermal masses tuned to lQCD thermodynamics. Such a model is able to describe the main feature of the non-perturbative dynamics: the enhancement of the interaction strength near $T_c$. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the nuclear suppression fact…
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We have developed a hydrodynamic model to study sequential melting of charmonium states in an expanding QGP medium. According to the initial fluid temperature profile, $J/ψ$'s are randomly distributed in the transverse plane. As the fluid evolve in time, the free streaming $J/ψ$'s are suppressed if the local fluid temperature exceed a critical temperature. PHENIX data on the centrality dependence of $J/ψ$ suppression in Au+Au collisions at mid-rapidity are explained by sequential melting of the charmonium states, $χ_c$, $ψ\prime$ and $J/ψ$, in the expanding medium. The critical temperatures $T…
We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium …
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）
A kinetic-rate equation approach in a thermally expanding medium is employed to calculate the evolution of charmonium and bottomonium distributions in heavy-ion collisions. The equilibrium properties of the quarkonia are taken from in-medium spectral functions which are schematically constrained by euclidean correlators from lattice QCD. The initial conditions for the rate equation (heavy-flavor cross sections, nuclear absorption) and the thermal evolution are constrained by data as available. After fixing two free parameters to describe charmonium data at SPS and RHIC, the predictions for LHC…
Charm-hadrons possess versatile hadro-chemistry as characterized by various transverse-momentum-dependent ratios between their different species. In particular, the charm hadro-chemistry may be modified in relativistic heavy-ion collisions with respect to proton-proton collisions at the same energy, as caused by novel diffusion and hadronization mechanisms of charm quarks in the environment of the created quark-gluon plasma (QGP) in the former. Inspired by recent measurements of leptons from charm-hadron decays (separated from bottom decays) in Pb-Pb and Au-Au collisions, we investigate the ef…
We discuss kinematical correlations between charged leptons from semileptonic decays of open charm/bottom, leptons produced in the Drell-Yan mechanism as well as some other mechanisms not included so far in the literature in proton-proton scattering at BNL RHIC. The distributions of charm and bottom quarks/antiquarks are calculated in the framework of the $k_t$-factorization approach. For this calculation we use the Kwieciński unintegrated parton distributions. The hadronization of heavy quarks is done by means of Peterson et al. fragmentation function. We use semileptonic decay functions foun…
We update the study of the total Psi and Upsilon production cross section in proton-proton collisions at RHIC energies using the QCD-based Color-Singlet (CS) Model, including next-to-leading order partonic matrix elements. We also include charm-quark initiated processes which appear at leading order in alpha_s, but which have so far been overlooked in such studies. Contrary to earlier claims, we show that the CS yield is consistent with measurements over a broad range of J/Psi rapidities. We also find that charm-quark initiated processes, including both intrinsic and sea-like charm components,…
We study the diffusion of charm quarks in the early stage of high energy nuclear collisions at the RHIC and the LHC. The main novelty of the present study is the introduction of the color current carried by the heavy quarks that propagate in the evolving Glasma (Ev-Glasma), that is responsible of the energy loss via polarization of the medium. We compute the transverse momentum broadening, $σ_p$, of charm in the pre-thermalization stage, and the impact of the diffusion on the nuclear modification factor in nucleus-nucleus collisions. The net effect of energy loss is marginal in the pre-thermal…
Within the Hadron-String Dynamics (HSD) transport approach we study the suppression pattern of charmonia at RHIC with respect to centrality and rapidity employing various model concepts such as variants of the 'comover absorption' model or the 'charmonium melting' scenario. We find that especially the ratio of the forward to mid-rapidity nuclear modification factors of J/Psi (R_AA (forward) / R_AA (mid)) cannot be explained by the interactions with 'formed' comoving mesons or by the 'color screening mechanism' alone. Only when incorporating interactions of the c or c-bar quark with a pre-hadro…
The observation of multi-particle azimuthal correlations in high-energy small-system collisions has led to intense debate on its origin and the possible coexistence from two competing theoretical scenarios: one based on initial-state intrinsic momentum anisotropy (ISM), and the other based on final-state collective response to the collision geometry (FSM). To complement the previous scan of asymmetric collision systems ($p$+Au, $d$+Au and He+Au), we propose a scan of small symmetric collision systems at RHIC, such as C+C, O+O, Al+Al and Ar+Ar $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV, to provide furthe…
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.
A compilation of recently measured STAR data for elliptic flow ($v_{2}$) of $ϕ$ mesons in RHIC Beam Energy Scan program and comparison with a multiphase transport model (AMPT) has been presented. The experimental data at $\sqrt{s_{NN}}$ $\geq$ 19.6 GeV agrees well with string melting version of the AMPT model. The model includes partonic interactions and quark coalescence as a mechanism of hadronization. This indicates that there is a substantial contribution to collectivity from partonic interactions at $\sqrt{s_{NN}}$ $\geq$ 19.6 GeV. The measured $ϕ$-meson $v_{2}$ at $\sqrt{s_{NN}}$ = 7.7 a…
We study the effect of thermal charm production on charmonium regeneration in high energy nuclear collisions. By solving the kinetic equations for charm quark and charmonium distributions in Pb+Pb collisions, we calculate the global and differential nuclear modification factors $R_{AA}(N_{part})$ and $R{AA}(p_t)$ for $J/Ψ$s. Due to the thermal charm production in hot medium, the charmonium production source changes from the initially created charm quarks at SPS, RHIC and LHC to the thermally produced charm quarks at Future Circular Collider (FCC), and the $J/Ψ$ suppression ($R_{AA}<1$) observe…
Thermalization and collective flow of charm (c) and bottom (b) quarks are evaluated from elastic parton scattering via "D"- and "B"-meson resonances in an expanding, strongly interacting quark-gluon plasma at RHIC. Pertinent drag and diffusion coefficients are implemented into a relativistic Langevin simulation to compute transverse-momentum spectra and azimuthal flow asymmetries (v_2) of c- and b-quarks. Upon hadronization (including coalescence and fragmentation) and semileptonic D- and B-decays, the resulting electron spectra (R_{AA} and v_2) are compared to recent RHIC data.
We report recent results from a multiphase transport (AMPT) model on the azimuthal anisotropies of particle momentum distributions in heavy ion collisions at the Relativistic Heavy Ion Collider. These include higher-order anisotropic flows and their scaling, the rapidity dependence of anisotropic flows, and the elliptic flow of charm quarks.
We propose an empirical model to determine the form of energy loss of charm quarks due to multiple scatterings in quark gluon plasma by demanding a good description of production of D mesons and non-photonic electrons in relativistic collision of heavy nuclei at RHIC and LHC energies. Best results are obtained when we approximate the momentum loss per collision $Δp_T \propto α\, p_T$, where $α$ is a constant depending on the centrality and the centre of mass energy. Comparing our results with those obtained earlier for drag coefficients estimated using Langevin equation for heavy quarks we fin…
Charm quarks, owing to their large mass, are produced predominantly in the initial hard scatterings in heavy-ion collisions, and therefore can be a valuable tool for studying the early time dynamics of these collisions. The rapidity-odd directed flow at mid-rapidity in heavy-ion collisions originates from a tilt in the reaction plane of the thermalized medium caused by the asymmetry between the number of participants from projectile and target nuclei as a function of rapidity. Recently, it has been predicted that the slope of the directed flow at mid-rapidity for $D^0$ mesons, arising from the…
