Higher Flow Harmonics Research Articles

Open charm and beauty measurements from small to large systems

Heavy-flavor quarks (i.e. charm and beauty) are essential probes to investigate the properties of the quark-gluon plasma (QGP) created in ultrarelativistic heavy-ion collisions. The measurement of the nuclear modification factor (RAA) gives insight into the in-medium parton energy loss in heavy-ion collisions. Furthermore, the measurements of heavy-flavor elliptic flow (v2) provide crucial information about the degree of thermalization of heavy quarks in the QGP, the path-length dependence of heavy-quark in-medium energy loss, and possible recombination effects. The higher flow harmonics, such as the triangular flow (v3), provide further constraints on the effect of fluctuations in the initial state of the system. The measurements in proton-proton (pp) collisions allow for testing perturbative quantum chromodynamics (pQCD) calculations and are needed as a baseline for investigating the medium effects in heavy-ion collisions. In this contribution, recent results of open charm and beauty production measured with the ALICE detector are discussed.

Azimuthal anisotropy in Cu+Au collisions at sNN=200 GeV

The azimuthal anisotropic flow of identified and unidentified charged particles has been systematically studied in Cu+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV for harmonics $n=$ 1-4 in the pseudorapidity range $|\eta|<1$. The directed flow in Cu+Au collisions is compared with the rapidity-odd and, for the first time, the rapidity-even components of charged particle directed flow in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200~GeV. The slope of the directed flow pseudorapidity dependence in Cu+Au collisions is found to be similar to that in Au+Au collisions, with the intercept shifted toward positive $\eta$ values, i.e., the Cu-going direction. The mean transverse momentum projected onto the spectator plane, $\langle p_x\rangle$, in Cu+Au collision also exhibits approximately linear dependence on $\eta$ with the intercept at about $\eta\approx-0.4$, closer to the rapidity of the Cu+Au system center-of-mass. The observed dependencies find natural explanation in a picture of the directed flow originating partly due the "tilted source" and partly due to the rapidity dependent asymmetry in the initial density distribution. Charge-dependence of the $\langle p_x\rangle$ was also observed in Cu+Au collisions, indicating an effect of the initial electric field created by charge difference of the spectator protons in two colliding nuclei. The rapidity-even component of directed flow in Au+Au collisions is close to that in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ = 2.76 TeV, indicating a similar magnitude of dipole-like fluctuations in the initial-state density distribution. Higher harmonic flow in Cu+Au collisions exhibits similar trends to those observed in Au+Au and Pb+Pb collisions and is qualitatively reproduced by a viscous hydrodynamic model and a multi-phase transport model. For all harmonics with $n\ge2$ we observe an approximate scaling of $v_n$ with the number of constituent quarks.

Correlations of flow harmonics in 2.76A TeV Pb-Pb collisions

Using the event-by-event viscous hydrodynamics VISH2+1 with MC-Glauber, MC-KLN, and AMPT initial conditions, we investigate the correlations of flow harmonics, including the symmetric cumulants $SC^{v}(m, n)$, the normalized symmetric cumulants $NSC(m, n)$, and the Pearson correlation coefficients $C(v_{m}^{2}, v_{n}^{2})$ in 2.76A TeV Pb--Pb collisions. We find $SC^{v}(m, n)$ is sensitive to both initial conditions and the specific shear viscosity $\eta/s$. A comparison with the recent ALICE data show that our hydrodynamic calculations can qualitatively describe the data of $SC^{v}(3, 2)$ and $SC^{v}(4, 2)$ for various initial conditions, which demonstrate that $v_2$, $v_4$ are correlated and $v_2$, $v_3$ are anti-correlated. Meanwhile, the predicted symmetric cumulants $SC^{v}(5, 2)$, $SC^{v}(5, 3)$, and $SC^{v}(4, 3)$ reveal that $v_2$ and $v_5$, $v_3$ and $v_5$ are correlated, $v_3$ and $v_4$ are anti-correlated in most centrality classes. We also find $NSC^{v}(3, 2)$ and $C(v_{3}^{2}, v_{2}^{2})$, which are insensitive to $\eta/s$, are mainly determined by corresponding $NSC^{\varepsilon}(3, 2)$ and $C(\varepsilon_{3}^{2}, \varepsilon_{2}^{2})$ correlators from the initial state. In contrast, other $NSC^{v}(m, n)$ and $C(v_{m}^{2}, v_{n}^{2})$ correlators are influenced by both initial conditions and $\eta/s$, which illustrates the non-linear mode couplings in higher flow harmonics with $n \geq 4$.

Nonlinear hydrodynamic response confronts LHC data

Higher harmonics of anisotropic flow (vn with n≥4) in heavy-ion collisions can be measured either with respect to their own plane, or with respect to a plane constructed using lower-order harmonics. By assuming that higher flow harmonics are the superposition of medium nonlinear and linear responses to initial anisotropies, we propose a set of nonlinear response coefficients χn's, which are independent of initial state by construction. In experiments, χn's can be extracted as the ratio between higher order harmonic flow measured in the plane constructed by v2 and v3, and moments of lower order harmonic flow. Simulations with single-shot hydrodynamics and AMPT model lead to results of these nonlinear response coefficients in good agreement with the experimental data at the LHC energy. Predictions for v7 and v8 measured with respect to plane of lower order harmonics are given accordingly.

Higher harmonic anisotropic flow of identified particles in Pb–Pb collisions with the ALICE detector

Anisotropic flow plays a crucial role in establishing the equation of state of the Quark Gluon Plasma. The results at RHIC and LHC have demonstrated that the matter created in heavy-ion collisions behaves as a nearly perfect fluid reflected in the low value of the shear viscosity over entropy density ratio (η/s). The higher flow harmonics are particularly sensitive to the value of η/s in hydrodynamic calculations. In this analysis, we present the first ALICE results on the pT differential v2, v3 and v4 for π±,K±,p(p‾) from the high statistics 2011 heavy-ion run. We investigate how these vn coefficients evolve with particle mass and centrality for the 0–1% and 20–30% centrality ranges. These new measurements aim at differentiating between models that use different initial conditions, constraining further the value of η/s and allowing to decouple the influence of the late hadronic stage from the hydrodynamic evolution of the system.

Generation of higher flow harmonics in Pb+Pb collisions at LHC in HYDJET++ model

The influence of elliptic and triangular flow on higher flow harmonics is studied within the HYDJET++ model, which merges parametrized hydro with jet quenching. Even harmonics can be generated by elliptic flow only, while odd harmonics need nonzero triangular component. A hydrodynamical model predicts a scaling of υ 4 /υ 2 2 ratio with pT , while jets force a rise of the high pT tail of the ratio. Hexagonal flow appears to be an interesting interplay between υ 2 and υ 3 . It shows a dominant contribution of υ 3 in central events and υ 2 at more peripheral collisions. Comparison with ALICE, ATLAS and CMS experimental data is presented.

Ultra-relativistic heavy-ion collisions - a hot cocktail of hydrodynamics, resonances and jets

Ultra-relativistic heavy-ion collisions at energies of RHIC and LHC are con- sidered. For comparison with data the HYDJET++ model, which contains the treatment of both soft and hard processes, is employed. The study focuses mainly on the interplay of ideal hydrodynamics, final state interactions and jets, and its influence on the devel- opment of harmonics of the anisotropic flow. It is shown that jets are responsible for violation of the number-of-constituent-quark (NCQ) scaling at LHC energies. The inter- play between elliptic and triangular flows and their contribution to higher flow harmonics and dihadron angular correlations, including ridge, is also discussed.

Two particle correlation measurements at PHENIX

Measurements of two particle azimuthal correlations in relativistic heavy ion collisions are useful tools to dissect the interplay between hard-scattered partons and hot dense medium. Correlations with trigger particle selection relative to second order event plane are sensitive to the path-length dependence of parton energy loss and to the influence of the medium on jet for high and intermediate transverse momenta pairs, respectively. To study the parton-medium coupling, it is also crucial to obtain correlations with rejection of contributions from higher harmonic flow. We present current results of second order event plane dependent correlations as well as correlations in which contributions from higher harmonic flow have been excluded in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV measured by PHENIX.

Two particle correlation measurements with respect to higher harmonic event planes at PHENIX

Measurements of two particle azimuthal correlations in relativistic heavy ion collisions provide information of the possible interplay between hard–scattered partons and the hot–dense medium. Toward an understanding of parton-medium coupling, it is indispensable to obtain correlations where contributions from higher harmonic flow( v n ) are rejected. It is also important to produce correlation measurements where the trigger particle is selected relative to second and third order event planes. This enables us to explore path-length dependence of parton energy loss and the influence of the medium on the jets. We present the latest PHENIX results of correlations in which contributions from higher harmonic flow have been subtracted, as well as second and third order event plane-dependent correlations in Au+Au collisions at s N N = 200 GeV .

Initial state fluctuations and higher harmonic flow in heavy-ion collisions

A framework combining Yang-Mills dynamics of the pre-equilibrium glasma with relativistic viscous hydrodynamic evolution of the quark–gluon plasma and hadron gas phases is presented. Event-by-event fluctuations of nucleon positions and color charges are taken into account, leading to negative binomial fluctuations of gluon multiplicities. Experimental anisotropic flow coefficients v 2 – v 5 of charged hadron distributions in heavy-ion collisions at the Large Hadron Collider are well described. Furthermore, event-by-event distributions of v 2 , v 3 and v 4 measured by the ATLAS collaboration are reproduced.

The "soft ridge" — is it initial-state geometry or modified jets?

A same-side (SS, on azimuth ϕ) 2D peak in measured angular correlations from 200 GeV p-p collisions exhibits properties expected for jet formation. In more-central Au-Au collisions the SS peak becomes elongated on pseudorapidity η and the transverse momentum pt structure is modified. In the latter case the SS 2D peak has been referred to as a "Soft Ridge," and arguments have been presented that the elongated peak represents flow phenomena ("triangular" and "higher harmonic" flows), possibly related to the initial-state A-A geometry. In this presentation I demonstrate that "higher harmonic flows" are related to SS 2D peak properties and review evidence for a jet interpretation of the SS peak for all Au-Au centralities.

Event-by-event hydrodynamical simulations forsNN=200GeV Au+Au collisions and the correlation between flow coefficients and initial asymmetry measures

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, $v_3$, $v_4$ however overestimate the experimental data, more in the peripheral collisions than in the central collisions. Correlation between initial (spatial) asymmetry measures and flow coefficients are also studied. With exception of the elliptic flow, for all the higher flow coefficients ($v_n$,n=3-5), correlation is reduced with collision centrality. In peripheral collisions, higher flow coefficients are only weakly correlated to the asymmetry measures. Elliptic flow however, remains strongly correlated with initial eccentricity in all the collision centralities.

Azimuth multipoles versus minimum-bias jets in 2D angular correlations on η and ϕ

Angular correlations measured in p–p and heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) include a same-side (SS) 2D peak. In peripheral A–A and p–p collisions the SS peak properties are consistent with predicted minimum-bias jet correlations. However, in more-central Au–Au collisions the SS peak becomes elongated on pseudorapidity η. Arguments have been proposed to explain the SS peak η elongation in terms of possibly fluctuating initial-state geometry multipoles coupled with radial flow to produce final-state momentum-space multipoles. Such arguments are based on Fourier decomposition of 2D angular correlations projected onto 1D azimuth. In this analysis we show that measured correlation structure on η (large curvatures) establishes a clear distinction between the SS 2D (jet) peak and 1D multipoles. Measured 2D peak systematics can predict inferred 1D Fourier amplitudes interpreted as ‘higher harmonic flows’. However, 1D Fourier amplitudes alone cannot describe 2D angular correlations. The SS 2D peak remains a unique structure that can be interpreted in terms of parton scattering and fragmentation in all cases.

Challenging claims of nonjet “higher harmonic” components in 2D angular correlations from high-energy heavy-ion collisions

It is conjectured that several higher harmonic flows $v_m$ may result from initial-state geometry fluctuations in \aa collisions coupled to a radially-expanding medium. But as with "elliptic flow" $v_2$ measurements, non-hydrodynamic mechanisms such as jet production may contribute to other higher azimuth multipoles $v_m$ as biases. Careful distinctions should be maintained between jet-related and nonjet (possibly hydrodynamic) contributions to $v_m$ (e.g., "nonflow" and "flow"). In this study we consider several questions: (a) To what extent do jet-like structures in two-dimensional (2D) angular correlations contribute to azimuth multipoles inferred from various $v_m$ methods? (b) If a multipole element is added to a 2D fit model is a nonzero amplitude indicative of a corresponding flow component? and (c) Can 2D correlations establish the necessity of nonjet contributions to some or all higher multipoles? Model fits to 2D angular correlations are used to establish the origins of azimuth multipoles inferred from 1D projections onto azimuth or from nongraphical numerical methods. We find that jet-like angular correlations, and specifically a 2D peak at the angular origin consistent with jet production, constitute the dominant contribution to inferred higher multipoles, and the data do not {\em require} higher multipoles in isolation from the jet-like 2D peak. Inference of "higher harmonic flows" results from identifying certain nominally jet-like structure as flow manifestations through unjustified application of 1D Fourier series analysis. Although the peak structure at the angular origin is strongly modified in more-central collisions some properties remain compatible with relevant pQCD theory expectations for jet production.

Review of Soft Interactions and Multiparticle Correlations

Recent developments in the area of soft interactions and multiparticle correlations are reviewed, including higher harmonic flows conjectured to result from the initial-state geometry which might coincide with some jet-like correlation features in more-central A-A collisions.

Femtoscopy of the system shape fluctuations in heavy-ion collisions

Dipole, triangular and higher harmonic flows that have an origin in the initial density fluctuations have gained a lot of attention as they can provide additional important information about the dynamical properties (e.g. viscosity) of the system. The fluctuations in the initial geometry should also be reflected in the detailed shape and velocity field of the system at freeze-out. In this talk, I discuss the possibility of measuring such fluctuations by means of identical and non-identical particle interferometry.