Flow in heavy ion collisions Urs Achim Wiedemann

Flow in heavy ion collisions Urs Achim Wiedemann CERN PH-TH Latsis-Symposium, 5 June 2013, Zurich

Heavy Ion Experiments

Elliptic Flow: hallmark of a collective phenomenon Compilation ALICE, PRL 105, 252302 (2010)

Particle production w. r. t. reaction plane Consider single inclusive particle momentum spectrum Particle with momentum p b To characterize azimuthal asymmetry, measure n-th harmonic moment of f(p). n-th order flow Problem: This expression cannot be used for data analysis, since the orientation of the reaction plane is not known a priori.

How to measure flow? • “Dijet” process • Maximal asymmetry • NOT correlated to the reaction plane • Many 2 ->2 or 2 -> n processes • Reduced asymmetry • final state interactions • asymmetry caused not only by multiplicity fluctuations • collective component is correlated to the reaction plane • NOT correlated to the reaction plane The azimuthal asymmetry of particle production has a collective and a random component. Disentangling the two requires a statistical analysis of finite multiplicity fluctuations.

Measuring flow – one procedure ● Want to measure particle production as function of angle w. r. t. reaction plane But reaction plane is unknown. . . ● Have to measure particle correlations: “Non-flow effects” But this requires signals ● Improve measurement with higher cumulants: This requires signals Borghini, Dinh, Ollitrault, PRC (2001)

● Momentum space v 2 @ LHC Reaction plane • Signal implies 2 -1 asymmetry of particles production w. r. t. reaction plane. • ‘Non-flow’ effect for 2 nd order cumulants do not characterize solely collectivity. Strong Collectivity ! p. T-integrated v 2

The appropriate dynamical framework ● depends on mean free path (more precisely: depends on applicability of a quasi-particle picture) Theory tools: System Free streaming p+p Particle cascade (QCD transport theory) Dissipative fluid dynamics Perfect fluid dynamics ? ? … p. A …? ? … AA … ? ?

The limiting case of perfect fluid dynamics (n comp. ) (5 comp. ) Equations of motion (n constraints) (4 constraints) closed by equation of state (1 constraint) Dynamical input: - Initial conditions (uncertainty) - QCD Equation of state (from Lattice QCD) - Decoupling (uncertainty) Wuppertal-Budapest, ar. Xiv: 1005. 3508, ar. Xiv: 1007. 2580

Viscous fluid dynamics Characterizes dissipative corrections in gradient expansion (4 n comp. ) (10 comp. ) To close equation of motion, supplement conservation laws and eos (n constraints) (4 constraints) (1 constraint) by point-wise validity of 2 nd law of thermodynamics The resulting Israel-Stewart relativistic fluid dynamics depends in general on relaxation times and transport coefficients.

Elements of fluid dynamic simulations Initialization of thermo-dynamic fields, e. g. Fluid-dynamic evolution: Sound attenuation length governs dominant dissipative mode Pics by B. Schenke final initial Decoupling: e. g. on space-time hypersurface , defined by, possibly followed by hadronic rescattering Cooper- Frye freeze-out

Fluid dynamical models of heavy ion collisions

Fluid dynamic prior to LHC - results Fluid dynamics accounts for: • Centrality dependence of elliptic flow • pt-dependence of elliptic flow • Mass dependence of elliptic flow (all particle species emerge from common flow field) • Single inclusive transverse momentum spectra at pt (< 3 Ge. V) In terms of fluid with minimal shear viscosity P. Romatschke ar. Xiv. 0902. 3663

Implications of minimal viscosity Back of envelope: For 1 -dim expanding fluid (Bjorken boost -invariant), entropy density increases like Isentropic “perfect liquid applies if Put in numbers Theory Minimal viscosity implies strongly coupled plasma. Importance of strong coupling techniques Arnold, Moore, Yaffe, JHEP 11 (2000) 001 Strong coupling limit of N=4 SYM Kovtun, Son, Starinets, hep -th/0309213

Phenomenological implication Minimal dissipation Maximal Transparency to Fluctuations decay on time scale, Models of the initial density distributions in AA-collisions show generically a set of event-by-event Eby. E fluctuations Fig from M. Luzum, ar. Xiv: 1107. 0592 Can we see how these spatial eccentricities propagate to asymmetries vn in momentum distributions?

Flow harmonics from particle correlations @ LHC Flow harmonics measured via particle correlations. Here: look directly at correlations of a ‘trigger’ with an ‘associate’ particle If flow dominated, then Characteristic features: 1. Small-angle jet-like correlations around (this is a ‘non-flow’ effect) 2. Long-range rapidity correlation (almost rapidity-independent ‘flow’) 3. Elliptic flow v 2 seems to dominate (for the semi-peripheral collisions shown here) 4. Away-side peak at is smaller (implies non-vanishing odd harmonics v 1, v 3, …) ATLAS prelim

Odd harmonics dominate central collisions In the most central 0 -5% events, Fluctuations in initial conditions dominate flow measurements

Flow as linear response to spatial asymmetries Characterize spatial eccentricities, e. g. , via moments of transverse density ALICE, ar. Xiv: 1105. 3865, PRL LHC data indicate: Spatial eccentricity is related approx. linearly to (momentum) flow

Hydrodynamics propagates Eby. E fluctuations • Fluid dynamics maps initial spatial eccentricities onto measured vn • 3+1 D viscous hydrodynamics with suitably chosen initial conditions reproduces v 2, v 3, v 4, v 5 in p. T and centrality B. Schenke, MUSIC, . QM 2012

Do smaller systems show flow: p. Pb? A fluid dynamical simulation of p. Pb@LHC yields P. Bozek, 1112. 0915 Fluid dynamics compares surprisingly well with in p. Pb@LHC. ATLAS, 1303. 2084 CMS, 1305. 0609

A (valid) analogy From a signal … via fluctuations …. …. to properties of matter Slide adapted from W. Zajc

How can non-abelian plasmas thermalize quickly? • Model-dependent in QCD but a rigorously calculable problem of numerical gravity in Ad. S/CFT • Very fast non-perturbative isotropization M. Heller et al, PRL, 1202. 0981 • The first rigorous field theoretic set-up in which fluid dynamics applies at very short time scales Chesler, Yaffe, PRL 102 (2009) 211601 • These non-abelian plasma are unique in that they do not carry quasi-particle excitations: perturbatively require but

To sum up • Flow measurements provide an abundant and generic manifestation of collective dynamics in heavy ion collisions. • Fluctuation analyses are still at the beginning. Directions currently explored include: system size dependence, event-shape engineering, mode-by-mode hydrodynamics • My apologies for not attempting to cover or connect important other developments in the field of relativistic heavy ion physics (jet quenching, quarkonia physics, thermal photon spectra, open heavy flavor, …, LPV)

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