Matthew Luzum

Triangular flow in hydrodynamics and transport theory

In ultrarelativistic heavy-ion collisions, the Fourier decomposition of the relative azimuthal angle, {Delta}{phi}, distribution of particle pairs yields a large cos(3{Delta}{phi}) component, extending to large rapidity separations {Delta}{eta}>1. This component captures a significant portion of the ridge and shoulder structures in the {Delta}{phi} distribution, which have been observed after contributions from elliptic flow are subtracted. An average finite triangularity owing to event-by-event fluctuations in the initial matter distribution, followed by collective flow, naturally produces a cos(3{Delta}{phi}) correlation. Using ideal and viscous hydrodynamics and transport theory, we study the physics of triangular (v{sub 3}) flow in comparison to elliptic (v{sub 2}), quadrangular (v{sub 4}), and pentagonal (v{sub 5}) flow. We make quantitative predictions for v{sub 3} at RHIC and LHC as a function of centrality and transverse momentum. Our results for the centrality dependence of v{sub 3} show a quantitative agreement with data extracted from previous correlation measurements by the STAR collaboration. This study supports previous results on the importance of triangular flow in the understanding of ridge and shoulder structures. Triangular flow is found to be a sensitive probe of initial geometry fluctuations and viscosity.

Viscous Hydrodynamic Predictions for Nuclear Collisions at the LHC

Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v2 in square root(s) = 5.5 TeV lead-lead and square root(s) = 14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v2 from RHIC to Pb+Pb at LHC, and v2 approximately 0 in p+p collisions unless eta/s<0.08.

Determining initial-state fluctuations from flow measurements in heavy-ion collisions

We present a number of independent flow observables that can be measured using multiparticle azimuthal correlations in heavy-ion collisions. Some of these observables are already well known, such as v{sub 2}(2) and v{sub 2}(4), but most are new--in particular, joint correlations among v{sub 1}, v{sub 2}, and v{sub 3}. Taken together, these measurements will allow for a more precise determination of the medium properties than is currently possible. In particular, by taking ratios of these observables, we construct quantities that are less sensitive to the hydrodynamic response of the medium and thus more directly characterize the initial-state fluctuations of the event shape, which may constrain models for early-time, nonequilibrium QCD dynamics. We present predictions for these ratios using two Monte Carlo models and compare them to available data.

Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions

We argue that the traditional event-plane method, which is still widely used to analyze anisotropic flow in ultrarelativistic heavy-ion collisions, should be abandoned because flow fluctuations introduce an uncontrolled bias in the measurement. Instead, one should use an alternative, such as the scalar-product method or cumulant method, which always measures an unambiguous property of the underlying anisotropic flow and therefore eliminates this bias, and does so without any disadvantages. It is known that this correction is important for precision comparisons of traditional v_n measurements requiring better than a few percent accuracy. However, we show that it is absolutely essential for correlations between different harmonics, such as those that have been recently measured by the ATLAS Collaboration, which can differ from the nominally-measured quantity by a factor two or more. We also describe how, using the corrected analysis method, the information from different subevents can be combined in order to optimize the precision of analyses.

Hydrodynamic predictions for 5.02 TeV Pb-Pb collisions

We make predictions for momentum-integrated elliptic and triangular flow as well as mean transverse momentum for 5.02 TeV Pb-Pb collisions, as planned at the Large Hadron Collider. We use hydrodynamic calculations to predict the change of these observables as the center-of-mass collision energy evolves from 2.76 TeV to 5.02 TeV per nucleon pair. By using previously measured values as a baseline, we are able to make a robust prediction without relying on a particular model for initial conditions and without precise knowledge of medium properties such as viscosity. Thus, though the predicted changes are small, they can provide a significant test of the current hydrodynamic picture of heavy-ion collisions.

Understanding anisotropy generated by fluctuations in heavy-ion collisions

Event-by-event fluctuations are central to the current understanding of ultrarelativistic heavy-ion collisions. In particular, fluctuations in the geometry of the early-time collision system are responsible for new phenomena such as triangular flow, which have solved important puzzles in existing data. We propose a simple model where initial fluctuations stem from independent flux tubes randomly distributed in the transverse plane. We calculate analytically the moments of the initial anisotropies (dipole asymmetry, eccentricity, triangularity), which are the sources of anisotropic flow, and their mutual correlations. Our analytic results are in good agreement with calculations from commonly-used Monte-Carlo codes, providing a simple understanding of the fluctuations contained in these models. Any deviation from these results in future experimental data would thus indicate the presence of non-trivial correlations between the initial flux tubes and/or extra sources of fluctuations that are not present in current models.

Solutions of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics

We use symmetry arguments developed by Gubser to construct the first radially-expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultra-relativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the MUSIC viscous hydrodynamics simulation code.

Anisotropic flow in event-by-event ideal hydrodynamic simulations of

We simulate top-energy Au+Au collisions using ideal hydrodynamics in order to make the first comparison to the complete set of midrapidity flow measurements made by the PHENIX Collaboration. A simultaneous calculation of v(2), v(3), v(4), and the first event-by-event calculation of quadrangular flow defined with respect to the v(2) event plane (v(4){Ψ(2)}) gives good agreement with measured values, including the dependence on both transverse momentum and centrality. This provides confirmation that the collision system is indeed well described as a quark-gluon plasma with an extremely small viscosity and that correlations are dominantly generated from collective effects. In addition, we present a prediction for v(5).

\sqrt{s_{NN}}=200

I compare the first viscous hydrodynamic prediction for integrated elliptic flow in Pb-Pb collisions at the Large Hadron Collider with the first data released by the ALICE Collaboration. These new data are found to be consistent with hydrodynamic extrapolations of the Relativistic Heavy-Ion Collider data with no change in medium parameters (e.g., average viscosity). I also discuss how, in general, a precise comparison of data to theoretical calculations requires an understanding of some subtleties of the measurement - most notably the cut on transverse momentum of the particles used and the differing sensitivities to flow fluctuations and nonflow effects of the various measurement methods.

GeV Au+Au collisions

We analyze published data from the ALICE Collaboration in order to obtain the first extraction of the recently proposed rapidity-even directed flow observable v(1). An accounting of the correlation due to the conservation of transverse momentum restores the factorization seen by ALICE in all other Fourier harmonics and thus indicates that the remaining correlation gives a reliable measurement of directed flow. We then carry out the first viscous hydrodynamic calculation of directed flow, and show that it is less sensitive to viscosity than higher harmonics. This allows for a direct extraction of the dipole asymmetry of the initial state, providing a strict constraint on the nonequilibrium dynamics of the early-time system. A prediction is then made for v(1) in Au-Au collisions at RHIC.