Collision-geometry fluctuations and triangular flow in heavy-ion collisions

We study how fluctuations in fluid dynamic fields can be dissipated or amplified within the characteristic spatio-temporal structure of a heavy ion collision. The initial conditions for a fluid dynamic evolution of heavy ion collisions may contain significant fluctuations in all fluid dynamical fields, including the velocity field and its vorticity components. We formulate and analyze the theory of local fluctuations around average fluid fields described by Bjorken's model. For conditions of laminar flow, when a linearized treatment of the dynamic evolution applies, we discuss explicitly how fluctuations of large wave number get dissipated while modes of sufficiently long wave-length pass almost unattenuated or can even be amplified. In the opposite case of large Reynold's numbers (which is inverse to viscosity), we establish that (after suitable coordinate transformations) the dynamics is governed by an evolution equation of non-relativistic Navier-Stokes type that becomes essentially two-dimensional at late times. One can then use the theory of Kolmogorov and Kraichnan for an explicit characterization of turbulent phenomena in terms of the wave-mode dependence of correlations of fluid dynamic fields. We note in particular that fluid dynamic correlations introduce characteristic power-law dependences in two-particle correlation functions.

Section: Jhep11(2011)100mentioning

confidence: 96%

Fluctuations around Bjorken flow and the onset of turbulent phenomena

Floerchinger

Wiedemann

2011

“…The study of v 2 at both the Relativistic Heavy Ion Collider (RHIC) and the LHC contributed significantly to the realisation that the produced system can be described as a strongly-coupled quark-gluon plasma (sQGP) with a small value of η/s, very close to the conjectured lower limit of 1/4π from AdS/CFT [12]. In addition, the overlap region of the colliding nuclei exhibits an irregular shape [8][9][10][11]13]. The irregularities originate from the initial density profile of nucleons participating in the collision, which is not isotropic and differs from one event to the other.…”

Section: Jhep09(2016)164mentioning

confidence: 99%

“…where E, N , p, p T , ϕ and η are the energy, particle yield, total momentum, transverse momentum, azimuthal angle and pseudorapidity of particles, respectively, and Ψ n is the azimuthal angle of the symmetry plane of the n th -order harmonic [8][9][10][11]. The n th -order flow coefficients are denoted as v n and can be calculated as 2) where the brackets denote an average over all particles in all events.…”

Section: Jhep09(2016)164mentioning

confidence: 99%

Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at s N N = 2.76 $$ \sqrt{s_{\mathrm{NN}}}=2.76 $$ TeV

Adam¹,

Adamová²,

Aggarwal³

et al. 2016

The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for π ± , K ± and p+p in Pb-Pb collisions at √ s NN = 2.76 TeV were measured with the ALICE detector at the Large Hadron Collider. The results were obtained with the Scalar Product method, correlating the identified hadrons with reference particles from a different pseudorapidity region. Effects not related to the common event symmetry planes (non-flow) were estimated using correlations in pp collisions and were subtracted from the measurement. The obtained flow coefficients exhibit a clear mass ordering for transverse momentum (p T ) values below ≈ 3 GeV/c. In the intermediate p T region (3 < p T < 6 GeV/c), particles group at an approximate level according to the number of constituent quarks, suggesting that coalescence might be the relevant particle production mechanism in this region. The results for p T < 3 GeV/c are described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses initial conditions generated by A Multi-Phase Transport model (AMPT) and describes the expansion of the fireball using a value of 0.08 for the ratio of shear viscosity to entropy density (η/s), coupled to a hadronic cascade model (UrQMD). Finally, expectations from AMPT alone fail to quantitatively describe the measurements for all harmonics throughout the measured transverse momentum region. However, the comparison to the AMPT model highlights the importance of the late hadronic rescattering stage to the development of the observed mass ordering at low values of p T and of coalescence as a particle production mechanism for the particle type grouping at intermediate values of p T for all harmonics.

“…central (head-on) collisions and the other v n coefficients in general are related to various shape components of the initial state arising from fluctuations of the nucleon positions in the overlap region [3]. The amplitudes of these shape components, characterized by eccentricities ǫ n , can be estimated via a simple Glauber model from the transverse positions (r, φ) of the participating nucleons relative to their centre of mass [4,5]:…”

Section: Jhep11(2013)183mentioning

confidence: 99%

Measurement of the distributions of event-by-event flow harmonics in lead-lead collisions at $ \sqrt{{{s_{NN }}}} $ = 2.76 TeV with the ATLAS detector at the LHC

Aad¹,

Abajyan²,

Abbott³

et al. 2013

217

197

The distributions of event-by-event harmonic flow coefficients v n for n = 2-4 are measured in √ s N N = 2.76 TeV Pb+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using charged particles with transverse momentum p T > 0.5 GeV and in the pseudorapidity range |η| < 2.5 in a dataset of approximately 7 µb −1 recorded in 2010. The shapes of the v n distributions suggest that the associated flow vectors are described by a two-dimensional Gaussian function in central collisions for v 2 and over most of the measured centrality range for v 3 and v 4 . Significant deviations from this function are observed for v 2 in mid-central and peripheral collisions, and a small deviation is observed for v 3 in mid-central collisions. In order to be sensitive to these deviations, it is shown that the commonly used multi-particle cumulants, involving four particles or more, need to be measured with a precision better than a few percent. The v n distributions are also measured independently for charged particles with 0.5 < p T < 1 GeV and p T > 1 GeV. When these distributions are rescaled to the same mean values, the adjusted shapes are found to be nearly the same for these two p T ranges. The v n distributions are compared with the eccentricity distributions from two models for the initial collision geometry: a Glauber model and a model that includes corrections to the initial geometry due to gluon saturation effects. Both models fail to describe the experimental data consistently over most of the measured centrality range. The ATLAS collaboration 41 IntroductionHeavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) create hot, dense matter that is thought to be composed of strongly interacting quarks and gluons. A useful tool to study the properties of this matter is the azimuthal anisotropy of particle emission in the transverse plane [1,2]. This anisotropy has been interpreted as a result of pressure-driven anisotropic expansion (referred to as "flow") of the created matter, and is described by a Fourier expansion of the particle distribution in azimuthal angle φ, around the beam direction:where v n and Φ n represent the magnitude and phase of the n th -order anisotropy of a given event in the momentum space. These quantities can also be conveniently represented by the per-particle "flow vector" [2]: ⇀ v n = (v n cos nΦ n , v n sin nΦ n ). The angles Φ n are commonly referred to as the event plane (EP) angles.In typical non-central [2] heavy ion collisions, the large and dominating v 2 coefficient is associated mainly with the "elliptic" shape of the nuclear overlap. However, v 2 in -1 - JHEP11(2013)183central (head-on) collisions and the other v n coefficients in general are related to various shape components of the initial state arising from fluctuations of the nucleon positions in the overlap region [3]. The amplitudes of these shape components, characterized by eccentricities ǫ n , can be estimated via a simple Glauber model from the...