Initial State Fluctuations Research Articles

ATLAS measurement of mean momentum fluctuations and correlations with the flow in Xe+Xe and Pb+Pb collisions

The thermal fluctuations in the QGP medium formed in heavy ion collisions present themselves as event-wise mean transverse momentum ([pT]) fluctuations in the final state. Recent studies have shown that the fluctuations are sensitive to radial flow, random thermal motion, and nuclear deformation. They can provide constraints on the extent of thermalization of the QGP droplet. Recently, correlations of [pT] with flow harmonic coefficients (vn) also gained interest, as they were found to be sensitive primarily to the initial state fluctuations. This talk presents precise measurements of up to 3rd order [pT] cumulants as a function of multiplicity and centrality with an emphasis on ultra-central collisions. These results have strong implications for understanding the impacts of the initial condition, medium thermalization, and medium properties on final state [pT] fluctuations.

Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plasmas to hadron distributions

It is an experimental fact that multi-particle correlations in the final states of high-energy nucleus-nucleus collisions are sensitive to collective correlations of nucleons in the wave functions of the colliding nuclei. Here, I show that this connection is more direct than it intuitively seems. With an energy deposition scheme inspired by high-energy quantum chromodynamics, and within a linearized description of initial-state fluctuations in the quark-gluon plasma, I exhibit relations between N-particle correlations in the final states of nuclear collisions and N-nucleon density distributions in the colliding nuclei. This result formally justifies the sensitivity of the outcome of high-energy collisions to features such as nuclear deformations. It paves the way, thus, to systematic studies of the impact of state-of-the-art nuclear interactions in such processes.

Probing initial geometrical anisotropy and final azimuthal anisotropy in heavy-ion collisions at Large Hadron Collider energies through event-shape engineering

Anisotropic flow is accredited to have effects from the initial state geometry and fluctuations in the nuclear overlap region. The elliptic flow (${v}_{2}$) and triangular flow (${v}_{3}$) coefficients of the final state particles are expected to have influenced by eccentricity (${ϵ}_{2}$) and triangularity (${ϵ}_{3}$) of the participants, respectively. In this work, we study ${v}_{2}$, ${v}_{3}$, ${ϵ}_{2}$, ${ϵ}_{3}$, and the correlations among them with respect to event topology in the framework of a multiphase transport model (AMPT). We use transverse spherocity and reduced flow vector as event shape classifiers in this study. Transverse spherocity has the unique ability to separate events based on geometrical shapes, i.e., jetty and isotropic, which pertain to pQCD and non-pQCD domains of particle production in high-energy physics, respectively. We use the two-particle correlation method to study different anisotropic flow coefficients. We confront transverse spherocity with a more widely used event shape classifier--reduced flow vector (${q}_{n}$) and they are found to have significant (anti)correlations among them. We observe significant spherocity dependence on ${v}_{2}$, ${v}_{3}$, and ${ϵ}_{2}$. This work also addresses transverse momentum dependent crossing points between ${v}_{2}$ and ${v}_{3}$, which varies for different centrality and spherocity percentiles.

Heavy-flavor anisotropic flow at RHIC and LHC energies within a full transport approach

The propagation of heavy quarks (HQs) in the quark-gluon plasma (QGP) is described by means of a full Boltzmann transport approach. The nonperturbative dynamics and the interaction between HQs and the bulk is taken into account by means of a Quasi-Particle Model. Including the intense electromagnetic and vortical fields, we discuss their impact on the directed flow of neutral D mesons at RHIC energy, clarifying the role of this observable in giving information on QGP transport properties. We also show a novel study of the correlations between different flow coefficients of D mesons and soft hadrons at LHC energy within a coalescence plus fragmentation hadronization scheme and including event-by-event initial state fluctuations. This investigations can put further constraints on HQ transport coefficients towards a solid determination in comparison to the lattice QCD calculations.

Signals of α clusters in 16O+16O collisions at the LHC from relativistic hydrodynamic simulations* *Supported in part by the National Natural Science Foundation of China (12075098, 12147101, 11875066, 11861131009), and Computations Were Performed at the Nuclear Science Computer Center at the CCNU (NSC3).

In relativistic heavy ion collisions, the fluctuations of initial entropy density convert to the correlations of final state hadrons in momentum space through the collective expansion of strongly interacting QCD matter. Using a (3+1)D viscous hydrodynamic program, CLVisc, we consider whether the nuclear structure, which provides initial state fluctuations as well as correlations, can affect the final state of heavy ion collisions, and whether one can find signals of α cluster structures in oxygen using final state observables in collisions at the CERN Large Hadron Collider. For the initial nucleon distributions in oxygen nuclei, we compare three different configurations, a tetrahedral structure with four-α clusters, the deformed Woods-Saxon distribution, and a spherical symmetric Woods-Saxon distribution. Our results show that the charged multiplicity as a function of centrality and the elliptic flow at the most central collisions using the four-α structure differs from those with the Woods-Saxon and deformed Woods-Saxon distributions, which may help to identify α clustering structures in oxygen nuclei.

Elliptic flow of charged particles at midrapidity relative to the spectator plane in Pb–Pb and Xe–Xe collisions

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons v2{ΨSP} in collisions of Pb ions at center-of-mass energy per nucleon–nucleon pair sNN=2.76 TeV and Xe ions at sNN=5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum for the 5–70% and 0.2–6 GeV/c ranges, respectively. The ratio between v2{ΨSP} and the elliptic flow coefficient relative to the participant plane v2{4}, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models describing the initial state fluctuations. A significant transverse momentum dependence of the ratio v2{ΨSP}/v2{4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state fluctuations. The ratios of v2{ΨSP} and v2{4} to the corresponding initial state eccentricities for Xe–Xe and Pb–Pb collisions at similar initial entropy density show a difference of (7.0±0.9)% with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark–gluon plasma produced in heavy-ion collisions at the LHC.

A Fourier-cumulant analysis for multiharmonic flow fluctuation

The Fourier analysis of the final particle distribution followed by cumulant study of the Fourier coefficient event-by-event fluctuation is one of the main approaches for testing the collective evolution in the heavy-ion collision. Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them. In particular, we show that there are 33 distinct cumulants with order 2, 3, 4, 5 and harmonics 2, 3, 4, 5. We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on T_mathtt{R}ENTo+VISH2+1+UrQMD. We compare the simulation with those normalized cumulants that the LHC has measured and predict the unmeasured ones. Comparing the initial and final state fluctuation normalized cumulants, we compute the linear and nonlinear hydrodynamic response couplings. We finally introduce the genuine three-particle correlation function containing information of all third-order cumulants.

Fluid velocity from transverse momentum spectra

We parametrize the transverse momentum distribution of outgoing hadrons in ultrarelativistic nucleus-nucleus collisions as a superposition of boosted thermal distributions. In this approach, which generalizes the conventional blast wave, the momentum distribution is determined by the distribution of the fluid velocity. We analyze the difference between this generalized blast-wave parametrization and a full hydrodynamic calculation. We then apply the generalized blast-wave fit to experimental data on Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76\ \mathrm{TeV}$. The fit is reasonable up to $p_t\sim 6\ \mathrm{GeV}$, much beyond the range where hydrodynamics is usually applied, but not perfect. Based on the differences between the fit and the data, we argue that an ideal hydrodynamic calculation cannot fit simultaneously all identified particle spectra, irrespective of the specific implementation. In particular, data display a significant excess of pions at low $p_t$, whose physical interpretation is discussed. Data also show that the distribution of the fluid velocity becomes broader as the collision becomes less central. This broadening is explained by event-by-event hydrodynamic calculations, where it results from the centrality dependence of initial-state fluctuations.

Measurements of mixed harmonic cumulants in Pb–Pb collisions at [formula omitted] TeV

Correlations between moments of different flow coefficients are measured in Pb–Pb collisions at sNN=5.02 TeV recorded with the ALICE detector. These new measurements are based on multiparticle mixed harmonic cumulants calculated using charged particles in the pseudorapidity region |η|<0.8 with the transverse momentum range 0.2<pT<5.0 GeV/c. The centrality dependence of correlations between two flow coefficients as well as the correlations between three flow coefficients, both in terms of their second moments, are shown. In addition, a collection of mixed harmonic cumulants involving higher moments of v2 and v3 is measured for the first time, where the characteristic signature of negative, positive and negative signs of four-, six- and eight-particle cumulants are observed, respectively. The measurements are compared to the hydrodynamic calculations using iEBE-VISHNU with AMPT and TRENTo initial conditions. It is shown that the measurements carried out using the LHC Run 2 data in 2015 have the precision to explore the details of initial-state fluctuations and probe the nonlinear hydrodynamic response of v2 and v3 to their corresponding initial anisotropy coefficients ε2 and ε3. These new studies on correlations between three flow coefficients as well as correlations between higher moments of two different flow coefficients will pave the way to tighten constraints on initial-state models and help to extract precise information on the dynamic evolution of the hot and dense matter created in heavy-ion collisions at the LHC.

Initial fluctuations and power spectrum of flow anisotropies in relativistic heavy-ion collisions

Flow has emerged as a crucial probe for the properties of the thermalized medium produced in relativistic heavy-ion collisions. The evolution of initial state fluctuations leaves imprints on the power spectrum of flow coefficients. Therefore, flow coefficients are a crucial probe of initial state fluctuations arising from the parton distributions of the colliding nuclei. This has a very strong correspondence with the physics of power spectrum of cosmic microwave background radiation (CMBR) anisotropies which directly probes initial inflationary fluctuations. Much work has been done to probe these interesting interconnections, in particular, in developing techniques for the measurements of higher flow coefficients. We present a short review of these developments. The effect of initial magnetic field on these features will also be reviewed. All this acquires special importance in view of upcoming electron-ion collider which will directly probe initial parton distribution of the colliding nucleus.

Probing granular inhomogeneity of a particle-emitting source by imaging two-pion Bose–Einstein correlations

Using the source imaging technique in two-pion interferometry, we study the image of the hydrodynamic particle-emitting source with the HIJING initial conditions for relativistic heavy-ion collisions on an event-by-event basis. It is shown that the initial-state fluctuations may give rise to bumpy structures of the medium during hydrodynamical evolution, which affects the two-pion emission space and leads to a visible two-tiered shape in the source function imaged using the two-pion Bose–Einstein correlations. This two-tiered shape can be understood within a similar but more analytic granular source model and is found to be closely related to the introduced quantity $$\xi$$ , which characterizes the granular inhomogeneity of the source. By fitting the imaged source function with a granular source parametrization, we extract the granular inhomogeneity of the hydrodynamic source, which is found to be sensitive to both the Gaussian smearing width of the HIJING initial condition and the centrality of the collisions.

Initial state fluctuations and the sub-leading flow modes from the experimental data and HYDJET++ model

A few microseconds after the birth of the Universe, the Universe was filled with the matter consisting of quarks and gluons, called quark gluon plasma (QGP). That primordial QGP lasts for about a few $$\upmu s$$ until the Universe cooled down and expanded enough that colored quarks had to confine within the colorless new formed hadrons. In high-energy nuclear collisions, where a high baryon density, or a high temperature could be achieved, small pieces of the QGP can be recreated and studied experimentally. Such created QGP undergoes an explosion, called the Little Bang. In spite of its small size (about 1000 $$fm^{3}$$ ) and short duration (a few fm/c, where c is the speed of light), the QGP is well described by relativistic hydrodynamics, including even the small perturbations on top of the explosion. In high-energy nucleus–nucleus (AA) collisions which have been performed at the Relativistic Heavy Ion Collider and at the Large Hadron Collider, the QGP was created with extremely high temperature and the baryon density close to zero. One of observables used to study QGP is azimuthal anisotropy. It was found that the initial state fluctuations have a significant influence on azimuthal anisotropies. We present results on azimuthal anisotropies measured in ultra-central PbPb collisions at $$\sqrt{s}_{NN}$$ = 2.76 TeV by the CMS and ALICE collaborations, as well as the leading and sub-leading flow modes for the elliptic and triangular anisotropies. The measured flow modes are also compared with the predictions from the HYDJET++ model.

Machine learning for high energy heavy ion collisions

The high energy heavy ion collision is a multi-stage process that is described by complex hybrid models. The initial state fluctuations in event-by-event simulations of heavy ion collisions convert to final state correlations by collective flow and hadronic cascade. It is not easy to design final state correlations (observables) from particles in momentum space, that can help to extract useful information, such as the initial state nuclear structure, the properties of quark gluon plasma and the nuclear equation of state. Machine learning is helpful in automatic feature extraction in heavy ion collisions. This article reviews the applications, challenges and possible future developments of machine learning in heavy ion physics.

Effects of initial state fluctuations on the mean transverse momentum

We show that in ideal hydrodynamic simulations of heavy-ion collisions, initial state fluctuations result in an increase of the mean transverse momentum of outgoing hadrons, 〈pt〉. Specifically, 〈pt〉 is larger by a few percent if realistic fluctuations are implemented than with smooth initial conditions, the multiplicity and impact parameter being kept fixed. We show that result can be traced back to the fact that for a given total entropy, the initial energy contained in the fluid is larger if the density profile is bumpy. We discuss the implication of these results for the extraction of the equation of state of QCD from experimental data.

Multiparticle correlation studies in pPb collisions at sNN=8.16 TeV

The second- and third-order azimuthal anisotropy Fourier harmonics of charged particles produced in pPb collisions, at $\sqrt{s_\mathrm{NN}} =$ 8.16 TeV, are studied over a wide range of event multiplicities. Multiparticle correlations are used to isolate global properties stemming from the collision overlap geometry. The second-order "elliptic" harmonic moment is obtained with high precision through four-, six-, and eight-particle correlations and, for the first time, the third-order "triangular" harmonic moment is studied using four-particle correlations. A sample of peripheral PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV that covers a similar range of event multiplicities as the pPb results is also analyzed. Model calculations of initial-state fluctuations in pPb and PbPb collisions can be directly compared to the high precision experimental results. This work provides new insight into the fluctuation-driven origin of the $v_3$ coefficients in pPb and PbPb collisions, and into the dominating overall collision geometry in PbPb collisions at the earliest stages of heavy ion interactions.

Study of the influence of initial-state fluctuations on hydrodynamic simulations

In this work, we are focusing on assessing the contribution of the initial-state fluctuations of heavy ion collision in the hydrodynamic simulations. We are trying to answer the question of whether the hydrodynamic simulation retains the same level of fluctuation in the final-state as for the initial stage. In another scenario, the hydrodynamic simulations of the fluctuation drowns in the final distribution of expanding matter. For this purpose, we prepared sufficient relativistic hydrodynamic program to study A+A interaction which allows analysing initial-state fluctuations in the bulk nuclear matter. For such an assumption, it is better to use high spatial resolution. Therefore, we applied the (3+1) dimensional Cartesian coordinate system. We implemented our program using parallel computing on graphics cards processors - Graphics Processing Unit (GPU). Simulations were carried out with various levels of fluctuation in initial conditions using the average method of events coming from UrQMD models. Energy density distributions were analysed and the contribution of fluctuations in initial conditions was assessed in the hydrodynamic simulation.

Charged-particle angular correlations in XeXe collisions at sNN=5.44 TeV

Azimuthal correlations of charged particles in xenon-xenon collisions at a center-of-mass energy per nucleon pair of $ \sqrt{s_{_\mathrm{NN}}} =$ 5.44 TeV are studied. The data were collected by the CMS experiment at the LHC with a total integrated luminosity of 3.42 $\mu$b$^{-1}$. The collective motion of the system formed in the collision is parameterized by a Fourier expansion of the azimuthal particle density distribution. The azimuthal anisotropy coefficients $v_{2}$, $v_{3}$, and $v_{4}$ are obtained by the scalar-product, two-particle correlation, and multiparticle correlation methods. Within a hydrodynamic picture, these methods have different sensitivities to non-collective and fluctuation effects. The dependence of the Fourier coefficients on the size of the colliding system is explored by comparing the xenon-xenon results with equivalent lead-lead data. Model calculations that include initial-state fluctuation effects are also compared to the experimental results. The observed angular correlations provide new constraints on the hydrodynamic description of heavy ion collisions.

Multiparticle correlations and higher order harmonics in pPb collisions at [formula omitted

The elliptic and higher-order azimuthal anisotropy Fourier harmonics (vn) are obtained for pPb collisions at sNN=8.16TeV over a wide range of event multiplicities based on multiparticle correlations. The data were collected by the CMS experiment during the 2016 LHC run. A sample of peripheral PbPb collisions at sNN=5.02TeV covering a similar range of event multiplicities to the pPb results is also analyzed for comparison. The ratios of different harmonic moments are obtained for both v2 and v3 with high precision, which allows a direct comparison to theoretical predictions assuming a hydrodynamic evolution of the created medium with initial-state density fluctuations, particularly probing the non-Gaussian nature of initial-state fluctuations in small collision systems. The presented results provide crucial insights into the origin of collective long-range correlations observed in small collision systems.

Transport properties from Charm to Bottom: pT suppression, anisotropic flow νn and their correlations to the bulk dynamics

We study the propagation of heavy quarks (HQs) in the quark-gluon plasma (QGP) by means of a relativistic Boltzmann transport (RBT) approach. The non-perturbative interaction between heavy quarks and light quarks is described by means of a quasi-particle approach able to describe simultaneously the experimental data for the nuclear suppression factor RAA and the elliptic flow ν2(pT) of D mesons from RHIC to LHC energies. In the same framework we predict the B meson nuclear modification factor at LHC. Finally, we discuss the relevance of initial state fluctuations that allows to extend the analysis to high order anisotropic flows νn(pT) as well as to investigate the role of QCD interaction in developing correlations between the light and the heavy flavour anisotropic flows.

Non-Gaussian elliptic-flow fluctuations in PbPb collisions at [formula omitted

Event-by-event fluctuations in the elliptic-flow coefficient v2 are studied in PbPb collisions at sNN=5.02 TeV using the CMS detector at the CERN LHC. Elliptic-flow probability distributions p(v2) for charged particles with transverse momentum 0.3<pT<3.0GeV/c and pseudorapidity |η|<1.0 are determined for different collision centrality classes. The moments of the p(v2) distributions are used to calculate the v2 coefficients based on cumulant orders 2, 4, 6, and 8. A rank ordering of the higher-order cumulant results and nonzero standardized skewness values obtained for the p(v2) distributions indicate non-Gaussian initial-state fluctuations. Bessel–Gaussian and elliptic power fits to the flow distributions are studied to characterize the initial-state spatial anisotropy.