The effects of fluctuating initial conditions are studied in the context of relativistic heavy ion collisions where a rapidly evolving system is formed. Two particle correlation analysis is applied to events generated with the NEXSPHERIO hydrodynamic code, starting with fluctuating non-smooth initial conditions (IC). Results show that the non-smoothness in the IC survives the hydro-evolution and can be seen as topological features of the angular correlation function of the particles emerging from the evolving system. A long range correlation is observed in the longitudinal direction and in the azimuthal direction a double peak structure is observed in the opposite direction to the trigger particle. This analysis provides clear evidence that these are signatures of the combined effect of tubular structures present in the IC and the proceeding collective dynamics of the hot and dense medium.
We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time $τ_π$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity $ν= η/sT$. We formulate methods for computing these correlations using second order dissipative hydrodynamics with noise. Current data are consistent with $τ_π/ν\sim 10$ but targeted measurements can improve this precision.
In this work, a hydrodynamic study of the di-hadron azimuthal correlations for the Au+Au collisions at 200 GeV is carried out. The correlations are evaluated using the ZYAM method for the centrality windows as well as the transverse momentum range in accordance with the existing data. Event-plane dependence of the correlation is obtained after the subtraction of contributions from the most dominant harmonic coefficients. In particular, the contribution from the triangular flow, $v_3$, is removed from the proper correlations following the procedure implemented by the STAR collaboration. The res…
In jet quenching, a hard QCD parton, before fragmenting into a jet of hadrons, deposits a fraction of its energy in the medium, leading to suppressed production of high-$p_T$ hadrons. Assuming that the deposited energy quickly thermalizes, we simulate the subsequent hydrodynamic evolution of the QGP fluid. Hydrodynamic evolution and subsequent particle emission depend on the jet trajectories. Azimuthal distribution of excess $π^-$ due to quenching jet, averaged over all the trajectories, reasonably well reproduce the di-hadron correlation as measured by the STAR and PHENIX collaboration in cen…
We will numerically investgate two-particle correlation function of CERN--SPS 158 A GeV Pb+Pb central collisions in detail based on a (3+1)-dimensional relativistic hydrodynamical model with first order phase transition. We use the Yano-Koonin-Podgoretski\uı parametrization as well as the usual Cartesian parametrization and analyze the pair momentum dependence of HBT radii extracted from the parametrizations. We find that the interpretation of the temporal radius parameters as the time duration in YKP parametrization is not available for the hydrodynamical model where the source became opaque …
Charge fluctuations for a baryon-neutral quark-gluon plasma have been calculated in lattice gauge theory. These fluctuations provide a well-posed rigorous representation of the quark chemistry of the vacuum for temperatures above T_c >~ 155 MeV. Due to the finite lifetime and spatial extent of the fireball created in relativistic heavy ion collisions, charge-charge correlations can only equilibrate for small volumes due to the finite time required to transport charge. This constraint leads to charge correlations at finite relative position that evolve with time. The source and evolution of suc…
We use a nonlinear response formalism to describe the event plane correlations measured by the ATLAS collaboration. With one exception ($\left\langle \cos(2Ψ_2 - 6Ψ_3 + 4 Ψ_4) \right\rangle$), the event plane correlations are qualitatively reproduced by considering the linear and quadratic response to the lowest cumulants. For the lowest harmonics such as $\left\langle \cos(2Ψ_2+3Ψ_3 - 5Ψ_5) \right\rangle$, the correlations are quantitatively reproduced, even when the naive Glauber model prediction has the wrong sign relative to experiment. The quantitative agreement for the higher plane corre…
In this work, we study the centrality as well as transverse momentum dependence of the dihadron correlation for Au+Au collisions at 200A GeV. The numerical simulations are carried out by using a hydrodynamical code NeXSPheRIO, where the initial conditions are obtained from a Regge-Gribov based microscopic model, NeXuS. In our calculations, the centrality windows are evaluated regarding multiplicity. The final correlations are obtained by the background subtraction via ZYAM methods, where higher harmonics are also considered explicitly. The correlations are evaluated for the 0 - 20\%, 20\%-40\%…
Correlations related to local charge conservation provide insight into the creation and evolution of up, down and strange charges in the quark-gluon plasma. Here, the evolution of charge correlations is overlaid onto a hydrodynamic calculation for the regions where temperature exceed 155 MeV, then transferred and carried through a microscopic model of the hadronic stage. Thus, for the first time, charge correlations are evolved consistently with a full state-of-the-art description of a heavy-ion collision. The charge correlations are projected onto charge balance functions, which characterize …
We calculate the squeezed back-to-back correlation (BBC) functions of $ϕϕ$ and $K^+K^-$ for heavy-ion collisions at RHIC and LHC energies, using ($2+1$)-dimensional hydrodynamics with fluctuating initial conditions. The BBC functions averaged over event-by-event calculations for many events for the hydrodynamic sources are smoothed as a function of the particle momentum. For heavy-ion collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV, the BBC functions are larger than those for collisions of Pb+Pb at $\sqrt{s_{NN}}=2.76$ TeV. The BBC of $ϕϕ$ may possibly be observed in peripheral collisions at th…
In the hot and dense hadronic sources formed in high-energy heavy-ion collisions, the particle interactions in medium might lead to a squeezed back-to-back correlation (BBC) of boson-antiboson pairs. We calculate the BBC functions of $ϕϕ$ for sources evolving hydrodynamically in ($2+1$) dimensions and with longitudinal boost invariance. The BBC functions for hydrodynamic sources exhibit oscillations as a function of the particle momentum because the temporal distributions of hydrodynamic sources have sharp falls to 0 at large evolving times. The dependences of the BBC functions on the directio…
The di-hadron angular correlation function is computed within boost invariant, ideal hydrodynamics for Au+Au collisions at $\sqrt{s}_{NN}=200$ GeV using Monte Carlo Glauber fluctuating initial conditions. When $0<p_T< 3$ GeV, the intensity of the flow components and their phases, $\left\{v_n, Ψ_n \right \}$ ($n=2,3$), are found to be correlated on an event by event basis to the initial condition geometrical parameters $\left\{\varepsilon_{2,n}, Φ_{2,n} \right \}$, respectively. Moreover, the fluctuation of the relative phase between trigger and associated particles, $Δ_n =Ψ_n^t - Ψ_n^a$, is fo…
The hydro-kinetic formalism has been used as a complementary approach to solving the Stochastic Differential Equations (SDE) corresponding to noisy hydrodynamics. The hydro-kinetic formalism consists of a deterministic set of relaxation type equations that tracks the evolution of 2-point correlation functions of stochastic hydrodynamic quantities. Hence they are comparatively easier to solve than the SDEs, which are computationally intensive and need to deal with arbitrarily large gradients. This work compares the two approaches for the propagation and diffusion of conserved charge fluctuation…
Measurements of di-hadron azimuthal correlations at different centralities for Au+Au collisions at 200 AGeV were reported by the PHENIX Collaboration. The data were presented for different ranges of transverse momentum. In particular, it was observed that the away-side correlation evolves from double- to a single-peak structure when the centrality decreases. In this work, we show that these features naturally appear as due to an interplay between the centrality-dependent smooth background elliptic flow and the one produced by event-by-event fluctuating peripheral tubes. To compare with the PHE…
Event-by-event hydrodynamics (or hydrodynamics with fluctuating initial conditions) has been developed in the past few years. Here we discuss how it may help to understand the various structures observed in two-particle correlations.
We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained …
Effects of dynamical long-range correlations over a fluid cell size scale on a relativistic fluid are discussed. It is shown that such correlations among the fluid elements introduced into hydrodynamical model induce some weak dissipation and viscosity into the fluid. The influence of the long-range correlations on the entropy current is also discussed.
Non-zero-range interactions are often incorporated into mean field theories through gradient terms. Here, a formalism is developed to incorporate such terms into hydrodynamics. These terms alter expressions for the entropy, chemical potential, temperature and the stress-energy tensor. The formalism respects local conservation of energy, charge and entropy. The formalism leads to static solutions where the temperature, chemical potential and hydrodynamic acceleration all vanish, even when the density profile might be non-uniform. Profiles for a phase boundary and for correlation functions are c…
We examine correlations of energy density induced by initial state fluctuations, which are localized in both transverse and longitudinal extent. The hotspots are evolved according to hydrodynamics in a background which includes radial flow. Two-point energy density correlations from these hotspots are computed as a function of the difference in azimuthal angle and rapidity. Such localized perturbations occur naturally in the theory of hydrodynamic fluctuations and may provide insight into some features of the two-particle correlation data from RHIC and the LHC.
A systematic study of HBT radii of pions, produced in heavy ion collisions in the intermediate energy regime (SPS), from an integrated (3+1)d Boltzmann+hydrodynamics approach is presented. The calculations in this hybrid approach, incorporating an hydrodynamic stage into the Ultra-relativistic Quantum Molecular Dynamics transport model, allow for a comparison of different equations of state retaining the same initial conditions and final freeze-out. The results are also compared to the pure cascade transport model calculations in the context of the available data. Furthermore, the effect of di…
We perform 3+1D viscous hydrodynamic calculations of proton-lead and lead-lead collisions at top LHC energy. We show that existing data from high-multiplicity p-Pb events can be well described in hydrodynamics, suggesting that collective flow is plausible as a correct description of these collisions. However, a more stringent test of the presence of hydrodynamic behavior can be made by studying the detailed momentum dependence of two-particle correlations. We define a relevant observable, $r_n$, and make predictions for its value and centrality dependence if hydrodynamics is a valid descriptio…
Event-by-event hydrodynamics, with fluctuating initial conditions, has shown to nicely reproduce several features of experimentally observed quantities in high-energy nuclear collisions. Here we discuss how it may help to understand, in a unified way, the various structures observed in the long-range two-particle correlations, both in nucleus-nucleus and p-p collisions. Suggestions of how experimentally this description could be tested are also discussed.
Thermal fluctuations affect the dynamics of systems near critical points, the evolution of the early universe, and two-particle correlations in heavy-ion collisions. For the latter, numerical simulations of nearly-ideal, relativistic fluids are necessary. The correlation functions of noise in relativistic fluids are calculated, stochastic integration of the noise in 3+1-dimensional viscous hydrodynamics is implemented, and the effect of noise on observables in heavy-ion collisions is discussed. Thermal fluctuations will cause significant variance in the event-by-event distributions of integrat…
It is argued that the observation of anisotropic azimuthal distribution of final state particles alone is insufficient to show whether the formed matter at RHIC behaves like hydrodynamic flow. Examining the intrinsic interaction (or correlation) of the formed matter should provide more definite judgement. To the end, a spatial-dependent azimuthal multiplicity-correlation pattern is suggested. It shows clearly in the pattern that there are two kinds of interactions at the early stage of Au + Au collisions at $\sqnn=200$ GeV generated by RQMD with hadron re-scattering and AMPT with string meltin…
In the context of event-by-event hydrodynamic description, we analyze the implications of two models characterized by distinct initial conditions. The initial energy density of the first model adopts a Gaussian-type distribution, while those of the second one are features by high energy peripheral tubes. We calibrate the initial conditions of both models so that their initial probability distribution of eccentricity are mostly identical. Subsequently, the resultant scaled probability distributions of collective flow and the correlations between flow harmonic and eccentricity coefficients are i…
The system formed in ultrarelativistic heavy-ion collisions behaves as a nearly-perfect fluid. This collective behavior is probed experimentally by two-particle azimuthal correlations, which are typically averaged over the properties of one particle in each pair. In this Letter, we argue that much additional information is contained in the detailed structure of the correlation. In particular, the correlation matrix exhibits an approximate factorization in transverse momentum, which is taken as a strong evidence for the hydrodynamic picture, while deviations from the factorized form are taken a…
In high energy heavy-ion collisions, the final anisotropic flow coefficients and their corresponding event-plane correlations are considered as the medium evolutional response to the initial geometrical eccentricities and their corresponding participant-plane correlations. We formulate a systematic theoretical analysis to study the hydrodynamical responses concerning higher order effects in Pb+Pb collisions at $\sqrt{s_\text{NN}}=2.76$ TeV by using Monte Carlo Glauber (MC-Glauber) model. To further understand the transformations of the initial participant-plane correlation, we construct a new …
Two-particle correlations in relative rapidity and azimuth are studied for the p-Pb collisions at the LHC energy of 5.02 TeV in the framework of event-by-event 3+1-dimensional viscous hydrodynamics. It is found that for the highest-multiplicity events the observed ridge structures appear in a natural way, suggesting that collective flow may be an important element in the evolution of the system. We also discuss the role of the charge balancing and the transverse-momentum conservation.
Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of unanticipated structure in the rapidity distribution of these fluctuations in the most central collisions. Although a first order classical Navier-Stokes theory can roughly explain the rapidity broadening, it cannot explain the additional structure. We propose that the rapidity structure can be explained using the second order causal Israel-Stewart hydrodynamics w…
The effects of event-by-event fluctuations in the initial geometry of the colliding nuclei are important in the analysis of final flow observables in relativistic heavy-ion collisions. We use hydrodynamic simulations to study the amplitude correlations between different orders of event-by-event fluctuating anisotropic flow harmonics. While the general trends seen in the experimental data are qualitatively reproduced by the model, deviations in detail, in particular for peripheral collisions, point to the need for more elaborate future calculations with a hybrid approach that describes the late…
We report on our recent attempt of quantitative modeling of the Chiral Magnetic Effect (CME) in heavy-ion collisions. We perform 3+1 dimensional anomalous hydrodynamic simulations on an event-by-event basis, with constitutive equations that contain the anomaly-induced effects. We also develop a model of the initial condition for the axial charge density that captures the statistical nature of random chirality imbalances created by the color flux tubes. Basing on the event-by-event hydrodynamic simulations for hundreds of thousands of collisions, we calculate the correlation functions that are …
We analyze the behavior of (net-)proton number cumulants in central collisions of heavy ions across a broad collision energy range by utilizing hydrodynamic simulations. The calculations incorporate essential non-critical contributions to proton fluctuations such as repulsive baryonic core and exact baryon number conservation. The experimental data are consistent with non-critical physics at collision energies $\sqrt{s_{\rm NN}} \geq 20$ GeV. The data from STAR and HADES Collaborations at lower collision energies indicate an excess of (multi-)proton correlations over the non-critical reference…
Formalism to calculate the hydrodynamic fluctuations by applying the Onsager theory to the relativistic Navier-Stokes equation is already known. In this work, we calculate hydrodynamic-fluctuations within the framework of the second order hydrodynamics of Müller, Israel and Stewart and its generalization to the third order. We have also calculated the fluctuations for several other causal hydrodynamical equations. We show that the form for the Onsager-coefficients and form of the correlation-functions remains same as those obtained by the relativistic Navier-Stokes equation and it does not dep…
Correlations of different azimuthal flow harmonics $v_n$ and symmetry planes $Ψ_n$ can add constraints to theoretical models, and probe aspects of the system that are independent of the traditional single-harmonic measurements. Using NeXSPheRIO, a hydrodynamical model which has accurately reproduced a large set of single-harmonic correlations at RHIC, we make predictions of these new observables for 200 A GeV Au+Au Collisions, providing an important baseline for comparison to correlations of flow harmonics, which contain non-trivial information about the initial state. We also point out how to…
We analyze correlations between the event-plane angles in different intervals of pseudorapidity within the 3+1-dimensional viscous hydrodynamics with the Glauber-model initial conditions. As predicted earlier, the fluctuations in the particle production mechanism in the earliest stage, together with asymmetry of the emission profiles in pseudorapidity from the forward- and backward going wounded nucleons, lead to the torque effect, namely, decorrelation of the event-plane angles in distant pseudorapidity bins. We use two- or three-bin measures of correlation functions to quantify the effect, w…
The recently measured correlations between the flow angles associated with higher harmonics in the anisotropic flow generated in relativistic heavy-ion collisions are shown to be of hydrodynamic origin. The correlation strength is found to be sensitive to both the initial conditions and the shear viscosity of the expanding fireball medium.
An analytically calculable model has been proposed recently for the simultaneous description of particle spectra and correlations, which is able to explain in a natural manner the $m_t$ scaling of the radius parameters of the Bose--Einstein correlation functions. We present here preliminary results on fitting this model to data sampled by NA44 collaboration in central S + Pb reactions at CERN SPS, which indicate that both pions and kaons freeze-out at a surprisingly low temperature of T approximately 108 MeV.
We investigate the effect of early chemical freeze-out on radial flow, elliptic flow and HBT radii by using a fully three dimensional hydrodynamic model. When we take account of the early chemical freeze-out, the space-time evolution of temperature in the hadron phase is considerably different from the conventional model in which chemical equilibrium is always assumed. As a result, we find that radial and elliptic flows are suppressed and that the lifetime and the spatial size of the fluid are reduced. We analyze the p_t spectrum, the differential elliptic flow, and the HBT radii at the RHIC e…
Recent measurements at the LHC involve the correlation of different azimuthal flow harmonics $v_n$. These new observables add constraints to theoretical models and probe aspects of the system that are independent of the traditional single-harmonic measurements such as 2- and multi-particle cumulants $v_n\{m\}$. Many of these new observables have not yet been measured at RHIC, leaving an opportunity to make predictions as a test of models across energies. We make predictions using NeXSPheRIO, a hydrodynamical model which has accurately reproduced a large set of single-harmonic correlations in a…
We study one-particle spectra and a two-particle correlation function in the 130 GeV/nucleon Au+Au collisions at RHIC by making use of a hydrodynamical model. We calculate the one-particle hadronic spectra and present the first analysis of Bose-Einstein correlation functions based on the numerical solution of the hydrodynamical equations which takes both longitudinal and transverse expansion into account appropriately. The hydrodynamical model provides excellent agreement with the experimental data in the pseudorapidity and the transverse momentum spectra of charged hadrons, the rapidity depen…
Centrality dependence of charged particles multiplicity, transverse momentum spectra, integrated and differential elliptic flow, in $\sqrt{s}_{NN}$=200 GeV Au+Au collisions are analyzed using event by event ideal hydrodynamics. Monte-Carlo Glauber model of initial condition, constrained to reproduce experimental charged particle's multiplicity in 0-10% Au+Au collisions, reasonably well reproduces all the experimental observables, e.g. centrality dependence of charged particles multiplicity, integrated and differential elliptic flow. Model predictions for higher flow harmonics, $v_3$, $v_4$ how…
$\textbf{HoTCoffeeh}$ ($\textbf{H}$anbury Br$\textbf{o}$wn-$\textbf{T}$wiss $\textbf{Co}$rrelation $\textbf{f}$unctions and radii $\textbf{f}$rom $\textbf{e}$vent-by-$\textbf{e}$vent $\textbf{h}$ydrodynamics) is a new computational tool which determines Hanbury Brown-Twiss (HBT) charged pion ($π^+$) correlation functions and radii for event-by-event (EBE) hydrodynamics with fluctuating initial conditions in terms of Cooper-Frye integrals, including resonance decay contributions. In this paper, we review the basic formalism for computing the HBT correlation functions and radii with resonance de…
Two-particle pseudorapidity correlations of hadrons produced in Pb+Pb collisions at 2.76 TeV at the CERN Large Hadron Collider are analyzed in the framework of a model based on viscous 3+1-dimensional hydrodynamics with the Glauber initial condition. Based on our results, we argue that the correlation from resonance decays, formed at a late stage of the evolution, produce significant effects. In particular, their contribution to the event averages of the coefficients of the expansion in the Legendre basis explain 60-70% of the experimental values. We have proposed an accurate way to compute th…
Instanton-dyons are topological solitons -- solutions of Yang-Mills equations -- which appear at non-trivial expectation value of $A_0$ at nonzero temperatures. Using the ensembles of those, generated in our previous work, for 2-color and 2-flavor QCD, below and above the deconfinement-chiral phase transition, we study the correlations between them, as well as fluctuations of several global charges in the sub-volumes of the total volume. The determined correlation lengths are the finite-$T$ extension of hadronic masses, such as that of $η'$ meson.
In this article, we briefly review the recent progress on collective flow and hydrodynamics in large and small systems at the Large Hadron Collider (LHC), which includes the following topics: extracting the QGP viscosity from the flow data, initial state fluctuations and final state correlations in 2.76 A TeV Pb--Pb collisions, correlations and collective flow in high energy p--Pb and p--p collisions.
The correlation between the harmonic flow and the transverse flow in relativistic heavy ion collisions is calculated in the hydrodynamic model. The partial correlation coefficient, corrected for fluctuations of multiplicity, is compared to experimental data. Estimators of the final transverse and harmonic flow are used to predict the value of the correlation coefficient from the moments of the initial distribution. A good description of the hydrodynamic simulation results is obtained if the estimator for the final transverse flow, besides the most important transverse size and entropy, include…
We present a dynamical description of (anti)proton number fluctuations cumulants and correlation functions in central Au-Au collisions at $\sqrt{s_{\rm NN}} = 7.7-200$ GeV by utilizing viscous hydrodynamics simulations. The cumulants of proton and baryon number are calculated in a given momentum acceptance analytically, via an appropriately extended Cooper-Frye procedure describing particlization of an interacting hadron resonance gas. The effects of global baryon number conservation are taken into account using a generalized subensemble acceptance method. The experimental data of the STAR col…
Correlation femtoscopy allows one to measure the space-time characteristics of particle production in relativistic heavy-ion collisions due to the effects of quantum statistics (QS) and final state interactions (FSI). The main features of the femtoscopy measurements at top RHIC and LHC energies are considered as a manifestation of strong collective flow and are well interpreted within hydrodynamic models employing equation of state (EoS) with a crossover type transition between Quark-Gluon Plasma (QGP) and hadron gas phases. The femtoscopy at lower energies was intensively studied at AGS and S…
The correlation between the mean transverse momentum of outgoing particles, $\langle p_t \rangle$, and the magnitude of anisotropic flow, $v_n$, has recently been measured in Pb+Pb collisions at the CERN Large Hadron Collider, as a function of the collision centrality. We confirm the previous observation that event-by-event hydrodynamics predicts a correlation between $v_n$ and $\langle p_t \rangle$ that is similar to that measured in data. We show that the magnitude of this correlation can be directly predicted from the initial condition of the hydrodynamic calculation, for $n=2,3$, if one re…
We propose that flow fluctuations have the same origin as transverse momentum fluctuations. The common source of these fluctuations is the spatially inhomogeneous initial state that drives hydrodynamic flow. Longitudinal correlations from an early Glasma stage followed by hydrodynamic flow quantitatively account for many features of multiplicity and $p_t$ fluctuation data. We develop a framework for studying flow and its fluctuations in this picture. We then compute elliptic and triangular flow fluctuations, and study their connections to the ridge.
