Event-plane Angles Research Articles

Forward-backward eccentricity and participant-plane angle fluctuations and their influences on longitudinal dynamics of collective flow

We argue that the transverse shape of the fireball created in heavy ion collision is controlled by event-by-event fluctuations of the eccentricity vectors for the forward-going and backward-going wounded nucleons: $\vec{\epsilon}_n^{\mathrm{F}}\equiv \epsilon_n^{\mathrm{F}} e^{i n\Phi_n^{\mathrm{*F}}}$ and $\vec{\epsilon}_n^{\mathrm{B}}\equiv \epsilon_n^{\mathrm{B}} e^{i n\Phi_n^{\mathrm{*B}}}$. Due to the asymmetric energy deposition of each wounded nucleon along its direction of motion, the eccentricity vector of the produced fireball is expected to interpolate between $\vec{\epsilon}_n^{\mathrm{F}}$ and $\vec{\epsilon}_n^{\mathrm{B}}$ along the pseudorapidity, and hence exhibits sizable forward-backward(FB) asymmetry ($\epsilon_n^{\rm B}\neq\epsilon_n^{\rm F}$) and/or FB-twist ($\Phi_n^{\mathrm{*F}}\neq\Phi_n^{\mathrm{*B}}$). A transport model calculation shows that these initial state longitudinal fluctuations for $n=2$ and 3 survive the collective expansion, and result in similar FB asymmetry and/or a twist in the final state event-plane angles. These novel EbyE longitudinal flow fluctuations should be accessible at RHIC and the LHC using the event-shape selection technique proposed in earlier papers. If these effects are observed experimentally, it could improve our understanding of the initial state fluctuations, particle production and collective expansion dynamics of the heavy ion collision.

Understanding non-linear hydrodynamic response in heavy-ion collisions via event-plane correlations

Recently the ATLAS collaboration measured correlations between pairs and triplets of event-plane angles in Pb+Pb collisions at =2.76 TeV and observed interesting centrality dependent patterns. In this work, the origin of these event-plane correlations and the quantative physical implications of their measured values are discussed. Such correlations can originate due to correlations between the eccentricities, ϵn, of different orders in the initial geometry. They can also be generated dynamically during the hydrodynamic expansion of the medium. Comparisons to a Glauber initial geometry model, and to AMPT transport model calculations show that the measured correlations are generated during hydrodynamic expansion of the medium. The measured correlations are shown to unambiguously establish that the higher order flow harmonics, v4-v6, are in fact largely driven by non-linear hydrodynamic response to lower order eccentricities ϵ2-ϵ3 of the initial geometry.

Method for studying the rapidity fluctuation and de-correlation of harmonic flow in heavy-ion collisions

An "event-shape twist" technique is proposed to study the longitudinal dynamics of harmonic flow, in particular the effects of rapidity fluctuation and event-plane decorrelation. This technique can distinguish between two types of rapidity decorrelation effects: a systematic rotation versus a random fluctuation of flow angles along the rapidity direction. The technique is demonstrated and the magnitude of the two decorrelation effects is predicted using the AMPT model via a single particle analysis and two-particle correlation analysis. An observed decorrelation can be attributed to a systematic rotation of event-plane angle along the pseudorapidity, consistent with a collective response to an initial state twist of the fireball proposed by Bozek {\it et.al.}. This rotation is also observed for several higher-order harmonics with the same sign and similar magnitudes.

Elliptic flow of thermal dileptons in event-by-event hydrodynamic simulation

The elliptic flows of thermal di-electrons are investigated within a (2+1)-dimension event-by-event hydrodynamic model for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The fluctuating initial conditions are given by the Monte Carlo Glauber model. We find in our event-by-event calculation rather weak correlation between the dilepton emission angles and the event plane angles of charged hadrons. We observe strong fluctuation effects in dilepton elliptic flows when using the event plane angles of dileptons at specific invariant mass $M$. The correlation between the dilepton event plane angle and charged hadron one becomes stronger with decreasing $M$. This provides a possible measure of the interplay between the effect of geometric deformation and that of fluctuating "hot spots" in relativistic heavy ion collisions.

Measurement of Event Plane Correlations in Pb–Pb Collisions at sNN=2.76TeV with the ATLAS Detector

A measurement of correlations between event-plane angles Φn is presented as a function of centrality for Pb–Pb collisions ant sNN=2.76TeV. These correlations are estimated from observed event-plane angles Ψn obtained from charged particle or transverse energy flow measured over a large pseudorapidity range |η|<4.8, followed by a resolution correction that accounts for the dispersion of Ψn relative to Φn. Various correlators involving two or three event planes with acceptable resolution are measured. Significant positive correlations are observed for 4(Φ2−Φ4),6(Φ2−Φ6),6(Φ3−Φ6),2Φ2+3Φ3−5Φ5,2Φ2+4Φ4−6Φ6 and −10Φ2+4Φ4+6Φ6. However, the measured correlations for 2Φ2+6Φ3+4Φ4 are negative. These results may shed light on the patterns of the fluctuation of the created matter in the initial state as well as the subsequent hydrodynamic evolution.

Elliptic and triangular flow and their correlation in ultrarelativistic high multiplicity proton–proton collisions at 14 TeV

The spatial configuration of initial partons in high multiplicity proton–proton scatterings at 14 TeV is assumed as three randomly positioned “hot spots”. The parton momentum distribution in the hot spots is calculated by HIJING2.0 with some modifications. This initial condition causes not only large eccentricity ϵ2 but also triangularity ϵ3 and the correlation of ϵ2−ϵ3 event-plane angles. The final elliptic flow v2, triangular flow v3, and the correlation of v2−v3 event-plane angles are calculated by using the parton cascade model BAMPS to simulate the space–time parton evolution. Our results show that the v2−v3 correlation is different from that of ϵ2−ϵ3. This finding indicates that translations of different Fourier components of the initial spatial asymmetry to the final flow components are not independent. A dynamical correlation between the elliptic and triangular flow appears during the collective expansion.

Longitudinal correlation of the triangular flow event plane in a hybrid approach with hadron and parton cascade initial conditions

The longitudinal long-range correlations of the triangular flow event plane angles are calculated in a Boltzmann + hydrodynamics hybrid approach. The potential to disentangle different energy deposition scenarios is explored by utilizing two different transport approaches for the early non-equilibrium evolution. In the hadronic transport approach the particle production in high energy heavy ion reactions is mainly governed by string excitation and fragmentation processes which are absent in the parton cascade approach. We find that in both approaches the initial state shows a strong longitudinal correlation of the event plane angles which is diluted but still persists in the final state momentum space distributions of the produced particles. A ridge-like structure can also be caused by near-collinear gluon radiation in a parton cascade approach and does not necessarily prove longitudinal flux tubes in the initial state.

Event-plane flow analysis without nonflow effects

The event-plane method, which is widely used to analyze anisotropic flow in nucleus-nucleus collisions, is known to be biased by nonflow effects,especially at high $p_t$. Various methods (cumulants, Lee-Yang zeroes) have been proposed to eliminate nonflow effects, but their implementation is tedious, which has limited their application so far. In this paper, we show that the Lee-Yang-zeroes method can be recast in a form similar to the standard event-plane analysis. Nonflow correlations are strongly suppressed by using the information from the length of the flow vector, in addition to the event-plane angle. This opens the way to improved analyses of elliptic flow and azimuthally-sensitive observables at RHIC and LHC.