Small System Collectivity in Relativistic Hadron and Nuclear Collisions
J. L. Nagle, W. A. Zajc
备注：
33 pages, 8 figures, 156 references. Invited review prepared for Annual Review of Nuclear and Particle Science 68 (2018). Version 2: Improved figures, references, corrected typos. Definitions of many quantities are now provided in margins
The bulk motion of nuclear matter at the ultra-high temperatures created in heavy-ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider is well described in terms of nearly inviscid hydrodynamics, thereby establishing this system of quarks and gluons as the most perfect fluid in nature. A revolution in the field is underway, spearheaded by the discovery of similar collective, fluid-like phenomena in much smaller systems including p+p, p+A, d+Au, and $^3$He$+$Au collisions. We review these exciting new observations and their implications.
We present the first full (3+1)D dynamical simulations of ultra-peripheral Pb+Pb collisions at the Large Hadron Collider. Extrapolating from p+Pb collisions, we explore whether a quasi-real photon $γ^*$ interacting with the lead nucleus in an ultra-peripheral collision can create a many-body system exhibiting fluid behavior. Assuming strong final-state interactions, we provide model results for charged hadron multiplicity, identified particle mean transverse momenta, and charged hadron anisotropic flow coefficients, and compare them with experimental data from the ALICE and ATLAS collaboration…
We briefly review highlights for ultra-relativistic light-heavy collisions (p-Pb, d-Au, 3He-Au, 12C-Au) which display collective evolution, with the same very characteristic features as in the A-A systems.
I explore weakly-collective singly-closed shell nuclei with high-j shells where active valence neutrons and particle-particle correlations may be the dominant collective degree of freedom. The combination of large and close-lying proton and neutron pairing gaps extracted from experimental masses seems to charaterize the origin of the weak collectivity observed in Ni and Sn superfluids with $N\approx Z$. The trend of $E2$ transition strengths, i.e., $B(E2; 2^+_1\rightarrow 0^+_1)$ values, in these nuclei is predicted from proton and neutron pairing-gap information. The agreement with the Ni iso…
Inelastic neutron scattering was used to study the low-lying nuclear structure of $^{132}$Xe. A comprehensive level scheme is presented, as well as new level lifetimes, multipole mixing ratios, branching ratios, and transition probabilities. Comparisons of these data as well as previously measured $E2$ strengths and $g$ factors are made with new shell-model calculations for $^{132,134,136}$Xe to explore the emergence of collectivity in the Xe isotopes with $N$ < 82 near the closed shell.
We study the multiplicity and rapidity dependence of thermal and prompt photon production in p+Pb collisions at 5.02 TeV, using a (3+1)D viscous hydrodynamic framework. Direct photon anisotropic flow coefficients $v^γ_{2,3}$ and nuclear modification factor $R^γ_\mathrm{pPb}(p_T)$ are presented in both the p-going (backward) and the Pb-going (forward) directions. The interplay between initial state cold nuclear effect and final state thermal enhancement at different rapidity regions is discussed. The proposed rapidity dependent thermal photon enhancement and direct photon anisotropic flow obser…
Nuclear collectivity and the harmonic spectrum of two-body correlations
Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS（巴黎萨克雷大学理论物理研究所）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；INFN-TIFPA Trento Institute of Fundamental Physics and Applications（特伦托基础物理与应用研究所）；Physics Division, Argonne National Laboratory（阿贡国家实验室物理部）；Computational Science Division, Argonne National Laboratory（阿贡国家实验室计算科学部）
Radioactive $^{129}$Sb, which can be treated as a proton plus semi-magic $^{128}$Sn core within the particle-core coupling scheme, was studied by Coulomb excitation. Reduced electric quadrupole transition probabilities, $B(E2)$, for the $2^+$ $\times$ $πg_{7/2}$ multiplet members and candidate $πd_{5/2}$ state were measured. The results indicate that the total electric quadrupole strength of $^{129}$Sb is a factor of 1.39(11) larger than the $^{128}$Sn core, which is in stark contrast to the expectations of the empirically successful particle-core coupling scheme. Shell-model calculations perf…
We present the measurement of centrality dependence of multi-strange hadron ($Ω$, $Ξ$ and $ϕ$) elliptic flow ($v_{2}$) at mid-rapidity in Au+Au collision at $\sqrt{s_{NN}}$ = 200 GeV. We investigate number-of-constituents quark (NCQ) scaling of identified hadrons $v_{2}$ for different collision centralities. Maximum deviation from ideal NCQ scaling observed at the level of 10% for centrality 30-80$%$ at $(m_{T} - m_{0})/n_{q}$ $>$ 0.6 GeV/$c^{2}$. This may indicate smaller contribution to the collectivity from the partonic phase in the peripheral collisions. We also observe the mass ordering o…
Signatures of collective behavior have been measured in highly relativistic p+p collisions, as well as in p+A, d+A, and 3He+A collisions. Numerous particle correlation measurements in these systems have been successfully described by calculations based on viscous hydrodynamic and transport models. These observations raise the question of the minimum necessary conditions for a system to exhibit collectivity. Recently, numerous scientists have raised the question of whether the quarks and gluons generated in e+e- collisions may satisfy these minimum conditions. In this paper we explore possible …
The emergence of nuclear collectivity near doubly-magic $^{132}$Sn was explored along the stable, even-even $^{124-130}$Te isotopes. Preliminary measurements of the $B(E2;4^{+}_{1}\rightarrow2^{+}_{1})$ transition strengths are reported from Coulomb excitation experiments primarily aimed at measuring the $g$ factors of the $4^{+}_{1}$ states. Isotopically enriched Te targets were excited by 198-205 MeV $^{58}$Ni beams. A comparison of transition strengths obtained is made to large-scale shell-model calculations with successes and limitations discussed.
We present full (3+1)D dynamical simulations to study collective behavior in ultra-peripheral nucleus-nucleus collisions (UPC) at the Large Hadron Collider (LHC) with the 3DGlauber+MUSIC+UrQMD framework. By extrapolating from asymmetric p+Pb collisions, we simulate a quasi-real photon $γ^*$ interacting with the Pb nucleus in an ultra-peripheral collision at the LHC, assuming strong final-state effects. We study the elliptic flow hierarchy between p+Pb and $γ^*$+Pb collisions, which is dominated by the difference in longitudinal flow decorrelations. Our theoretical framework provides a quantita…
Hanbury Brown--Twiss interferometry (HBT) provides crucial insights into both the space-time structure and the momentum-space evolution of ultrarelativistic nuclear collisions at freeze-out. In particular, the dependence of the HBT radii on the transverse pair momentum $K_T$ and the system charged multiplicity $dN_{\mathrm{ch}}/dη$ may reflect the mechanisms driving collective behavior in small systems. This paper argues that certain features observed in the multiplicity dependence of the HBT radii can be naturally understood if small systems evolve hydrodynamically at high-multiplicity. This …
We propose a test-particle method to probe the transport dynamics of the establishment and development of collective flow in large and small systems of heavy-ion collisions. We place test particles as passengers into the partonic medium created by Au$+$Au midcentral collisions at $\sqrt{s_{NN}}$ = 200 GeV and $p$ $+$ Pb central collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, using a multiphase transport model. With the help of test particles in two extreme test cases, we demonstrate that parton collisions play an important role in establishing and developing collectivity in large and small colliding…
The neutron-rich isotopes $^{58-63}$Cr were produced for the first time at the ISOLDE facility and their masses were measured with the ISOLTRAP spectrometer. The new values are up to 300 times more precise than those in the literature and indicate significantly different nuclear structure from the new mass-surface trend. A gradual onset of deformation is found in this proton and neutron mid-shell region, which is a gateway to the second island of inversion around \emph{N}=40. In addition to comparisons with density-functional theory and large-scale shell-model calculations, we present predicti…
Many-body nuclear theory utilizing microscopic or chiral potentials has developed to the point that collectivity might be dealt with in an {\it ab initio} framework without the use of effective charges; for example with the proper evolution of operators, or alternatively, through the use of an appropriate and manageable subset of particle-hole excitations. We present a precise determination of $E2$ strength in $^{22}$Mg and its mirror $^{22}$Ne by Coulomb excitation, allowing for rigorous comparisons with theory. No-core symplectic shell-model calculations were performed and agree with the new…
Proton Collectivity in Au+Au Collisions at $\sqrt{s_{\rm NN}}=2.4-4.5$~GeV from a Unified Purely Hadronic EOS without QCD Phase Transition
School of Physics and Electronic Science, Guizhou Normal University（贵州师范大学物理与电子科学学院）；Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University（贵州师范大学贵州省射电天文与数据处理重点实验室）；Department of Physics, Tsinghua University（清华大学物理系）；Center for High Energy Physics, Tsinghua University（清华大学高能物理中心）
A measurement for studying the mass dependence of the dilepton interferometry in relativistic heavy-ion collision experiments as a tool to characterize the quark-gluon phase is proposed. In calculations involving dileptons, we show that the mass dependence of radii extracted from the virtual photon (dilepton) interferometry provide access to the development of collective flow with time. It is argued that the non-monotonic variation of HBT radii with invariant mass of the lepton pairs signals the formation of quark gluon plasma in heavy ion collisions. Our proposal of experimentally measuring t…
In this paper, we investigate the hydrodynamic collectivity in proton--proton (pp) collisions at 13 TeV, using iEBE-VISHNU hybrid model with HIJING initial conditions. With properly tuned parameters, our model simulations can remarkably describe all the measured 2-particle correlations, including integrated and differential elliptic flow coefficients for all charged and identified hadrons ($K_S^0$, $Λ$). However, our model calculations show positive 4-particle cumulant $c_{2}\{4\}$ in high multiplicity pp collisions, and can not reproduce the negative $c_{2}\{4\}$ measured in experiment. Furth…
I give an overview of the latest development in understanding collective phenomena in high-multiplicity hadronic final state from relativistic nucleus-nucleus, proton-nucleus and proton-proton collisions. Upon reviewing the experimental data and confronting them with theoretical models, a unified paradigm in describing the observed collectivity across all hadronic collision systems is emerging. Potential future paths toward addressing key open questions, especially on collectivity in small systems (pp, pA), are discussed.
Medium modification of particle spectra and the origin of collectivity in small collision systems are widely debated topics in the heavy-ion community. To address these open questions, we propose the study of particle production and collectivity for varying system sizes,Au+Au $>$ Ru+Ru/Zr+Zr $>$ Cu+Cu $>$ d+Au $>$ $γ$+Au, available at RHIC using the STAR detector. We present the first measurements of centrality dependent charged hadron production in Isobar (Ru+Ru and Zr+Zr) collisions, including the nuclear modification factors ($R_\mathrm{AA}$) at high transverse momentom ($p_\mathrm{T}$), an…
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…
The exploration of the strong-interaction matter under extreme conditions is one of the main goals of relativistic heavy-ion collisions. We provide some of the main results on the novel properties of quark-gluon plasma, with particular focus given to the strong collectivity and the color opaqueness exhibited by such hot and dense matter produced in high-energy nuclear collisions at RHIC and the LHC.
Flow measurements of multi-strange baryons from Au + Au collisions at RHIC energies demonstrate that collectivity develops before hadronization, among partons. To pin down the partonic EOS of matter produced at RHIC, the status of thermalization in such collisions has to be addressed. We propose to measure collective flow of heavy-flavor quarks, e.g. charm quarks, as an indicator of thermalization of light flavors ($u,d,s$). The completion of the time of flight barrel and the proposed upgrade with a $μ$Vertex detector for heavy-flavor identification in STAR are well suited for achieving these …
Physics of Collectivity and EOS from the RHIC Beam Energy Scan Program
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Central China Normal University（华中师范大学）
PHENIX has measured elliptic and triangular flow of charged hadrons in $p/d/^{3}$He$+$Au collisions at a center-of-mass energy of 200 GeV per nucleon pair, and elliptic flow in $d$+Au collisions at 200, 62.4, and 39 GeV. In order to asses the origin of collectivity in the smallest systems, these results are compared with several theoretical models that produce azimuthal particle correlations based on initial and/or final state effects. Hydrodynamical models, which include the formation of a droplet of quark-gluon plasma, provide the best simultaneous description of our observations.
Collective flow of the final-state hadrons observed in ultrarelativistic heavy-ion collisions or even in smaller systems formed in high-multiplicity pp and p/d/$^3$He-nucleus collisions is one of the most important diagnostic tools to probe the initial state of the system and to shed light on the properties of the short-lived, strongly-interacting many-body state formed in these collisions. Limited, in the initial years, to the study of mainly the directed and elliptic flows -- the first two Fourier harmonics of the single-particle azimuthal distribution -- this field has evolved in recent yea…
We present a measurement of azimuthal correlations between inclusive J/$ψ$ and charged hadrons in p-Pb collisions recorded with the ALICE detector at the CERN LHC. The J/$ψ$ are reconstructed at forward (p-going, 2.03 $<$ y $<$ 3.53) and backward (Pb-going, $-$4.46 $<$ y $<$ $-$2.96) rapidity via their $μ^+μ^-$ decay channel, while the charged hadrons are reconstructed at mid-rapidity ($|η|$ $<$ 1.8). The correlations are expressed in terms of associated charged-hadron yields per J/$ψ$ trigger. A rapidity gap of at least 1.5 units is required between the trigger J/$ψ$ and the associated charge…
Imprints of octupole collectivity in uranium-238 on relativistic heavy-ion flow observables
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), and Institute of Modern Physics, Fudan University（复旦大学现代物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（复旦大学理论物理研究中心）；Department of Chemistry, Stony Brook University（石溪大学化学系）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理部）；Department of Physics and Astronomy, Wayne State University（韦恩州立大学物理与天文学系）；RIKEN BNL Research Center, Brookhaven National Laboratory（布鲁克海文国家实验室理研BNL研究中心）；Physics Department and Center for Particle Physics and Field Theory, Fudan University（复旦大学物理系及粒子物理与场论中心）
We review hadron production in heavy ion collisions with emphasis on pion and kaon production at energies below 2 AGeV and on partonic collectivity at RHIC energies.
The collective phenomena are observed not only in heavy ion collisions, but also in the proton-nucleus and in high-multiplicity $pp$ collisions. The latest results from this area obtained in ATLAS are presented. In $p$+Pb collisions the emission source of particles is measured using the HBT method. The analysis of $p$+Pb data collected in 2016 provides information on the elliptic flow of charged hadrons and muons. Low multiplicity events from $pp$, $p$+Pb and peripheral Pb+Pb collisions are studied with the cumulant methods. A deeper understanding of Pb+Pb collisions is provided by the analysi…
Features of collectivity observed in high energy A+A collision systems at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) imply a strongly coupled quark gluon plasma (QGP) that flows. One defining feature of collectivity is long-range angular correlations which are characterized experimentally by measuring the azimuthal anisotropy of particles well separated in rapidity. Evidence indicating long-range angular correlations include the appearance of the so-called near-side "ridge" in correlation functions and $p_T$ dependent flow components ($v_N$). These features …
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-…
In hadronic collisions, interference between different production channels affects momentum distributions of multi-particle final states. As this QCD interference does not depend on the strong coupling constant, it is part of the no-interaction baseline that needs to be controlled prior to searching for other manifestations of collective dynamics. Here, we introduce a model that is based on the QCD theory of multi-parton interactions and that allows one to study interference effects in the production of $m$ particles in hadronic collisions with $N$ parton-parton interactions ("sources"). In an…
With the aim of understanding the phase structure of nuclear matter created in high-energy nuclear collisions at finite baryon density, a beam energy scan program has been carried out at Relativistic Heavy Ion Collider (RHIC). In this mini-review, most recent experimental results on collectivity, criticality and heavy flavor productions will be discussed. The goal here is to establish the connection between current available data and future heavy-ion collision experiments in a high baryon density region.
The presence of correlations between particles significantly separated in pseudorapidity in proton-proton and proton-nucleus collisions revealed surprises in the early LHC data. Are the physical processes responsible for the observed long-range pseudorapidity correlations and their azimuthal structure the same in small collision systems as in heavy ion collisions? Whereas in the case of heavy ion collisions "flow" is interpreted as generated by initial geometric inhomogeneities, calculations indicate that initial-state momentum correlations are present and could contribute to the observed azim…
The azimuthal anisotropy parameter v2 has been measured with high statistics for identified hadrons in sqrt(s_NN) = 200 GeV Au+Au collisions with the STAR experiment. At high transverse momentum (pT) a strong v2 for pi+ + pi- and p + pbar is observed. In the intermediate pT region, number-of-constituent-quark scaling was tested to high precision. A detailed comparison of v2 for the multi-strange hadrons phi, Xi + anti-Xi, and Omega + anti-Omega with other particle species substantiates the development of collectivity among partons in the early phase of the collisions at RHIC.
We celebrate the legacies of our friend and mentor Professor Lianshou Liu who was one of the pioneers for the phenomenology of multi-particle interactions and initiated the physics of relativistic heavy-ion collisions in China. In this article, we discuss some of the recent exciting experimental observations on the collective phenomena including collectivity, chirality, criticality, strangeness production, and thermal equilibrium in high-energy nuclear collisions. Future directions, especially the physics at high baryon density, will be discussed with a focus on the first-order phase boundary …
I propose a scaling analysis of the hadron multiplicity ratio measured in Deep Inelastic Scattering on nuclear targets as a tool to distinguish energy loss and nuclear absorption effects on hadron suppression in cold nuclear matter. The proposed scaling variable is a function of the hadron fractional energy and of the virtual photon energy. Its functional form, which depends on a parameter λ, can be fixed by general theoretical considerations and encompasses both energy loss and absorption models. The parameter λis fitted to HERMES experimental data and shown to favor prehadron nuclear absorpt…
The problem of understanding the nuclear effects observed in lepton-nucleus deep-inelastic-scattering (the EMC effect) is still with us. Standard nuclear models (those using only hadronic degrees of freedom) are not able to account for the EMC effect. Thus it is necessary to understand how the nuclear medium modifies quark wave functions in the nucleus. Possibilities for such modifications, represented by the quark meson coupling model, and the suppression of point-like-configurations are discussed, and methods to experimentally choose between these are reviewed.
We argue that hadron production in coherent diffraction of proton on a heavy nucleus provides a very sensitive probe of the low-x QCD dynamics. This process probes the BFKL dynamics in proton and the non-linear gluon evolution in nucleus. We calculate the diffractive hadron production cross sections in the RHIC and LHC kinematic regions. To study the nuclear effects we introduce the diffractive nuclear modification factor. We show that unlike the nuclear modification factor for inclusive hadron production that has a very interesting dynamics at RHIC but is expected to be almost completely satu…
Using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, we investigate azimuthal correlations in p--Pb collisions at $\sqrt{s_{_{\rm NN}}}=5.02$ TeV. Comparison with the experimental data shows that UrQMD can not reproduce the multiplicity dependence of 2- and 4-particle cumulants, especially the transition from positive to negative values of $c_{2}\{4\}$ in high multiplicity events, which has been taken as experimental evidence of collectivity in p--Pb collisions. Meanwhile, UrQMD can not qualitatively describe the differential elliptic flow, $v_{2}(p_{\rm T})$, of all charged …
We study the effects of hadronic rescattering on hadron distributions in high-energy nuclear collisions by using an integrated dynamical approach. This approach is based on a hybrid model combining (3+1)-dimensional ideal hydrodynamics for the quark gluon plasma (QGP), and a transport model for the hadron resonance gas. Since the hadron distributions are the result of the entire expansion history of the system, understanding the QGP properties requires investigating how rescattering during the hadronic stage affects the final distributions of hadrons. We include multistrange hadrons in our stu…
PHENIX has performed an extensive study on the evolution of medium effects from small to large systems. PHENIX has continued searching for Quark-Gluon Plasma (QGP) in small systems by measuring collectivity, modification of light hadron and quarkonia production, and jet substructure. In large systems, detailed studies on the property of the QGP have been done using direct photon, $π^{0}$-hadron correlation, heavy-flavor electron, and $J/ψ$ flow with a large statistics of data collected in 2014. This report covers new results from the PHENIX experiment in various collision systems.
The experimental data for identified hadron spectra from pp,d+A and AA collisions are reviewed. Three regions with different dominant production mechanisms are considered: soft region (pt <2 GeV/c) - with large degree of collectivity and thermalization, hard particle production which exhibits jet-quenching in Au+Au collisions at RHIC and intermediate region (2 < pt <5 GeV/c) with distinct baryon dynamics. Cronin effect, nuclear modification factors and jet-like correlations are studied with the goal of understanding the baryon dynamics at RHIC.
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 investigate the binding energy per nucleon and hadron properties in infinite and homogeneous nuclear matter within the framework of the in-medium modified Skyrme model. We first consider the medium modifications of the single hadron properties by introducing the optical potential for pion fields into the original Lagrangian of the Skyrme model. The parameters of the optical potential are well fitted to the low-energy phenomenology of pion-nucleus scattering. Furthermore, the Skyrme term is also modified in such a way that the model reproduces bulk properties of nuclear matter, in particular…
After decades-long attempts to measure the mass shift and understand the origin of hadron mass, it became clear that one has to analyze hadrons with small vacuum width. Also, to identify the effect of chiral symmetry breaking, one has to start by looking at chiral partners. In this talk, I will review why such consideration inevitably led us to consider $K^*$ and $K_1$ in nuclear matter [T. Song, T. Hatsuda, S H Lee, PLB792 (2019) 160-169]. With the kaon beam at JPARC, one could observe the mass shift of both particles in a nuclear target experiment. Once the masses and mass difference of $K^*…
Proton-proton (pp) collisions have been traditionally used as a baseline measurement in the search for a deconfined state of matter in heavy-ion collisions at ultrarelativistic energies. The unprecedented collision energies that are available at the Large Hadron Collider (LHC) at the European Laboratory for Nuclear Research (CERN) have illuminated new challenges in understanding the possible formation of droplets of this deconfined matter of partonic degrees of freedom in hadronic collisions, especially in high-multiplicity events. Enhancement of multi-strange particles compared to pions, degr…
