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

2. Heavy Ion Experiments

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

4. Particle production w.r.t. reaction plane Particle with momentum p b Consider single inclusive particle momentum spectrum 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.

5. How to measure flow? “Dijet” process Maximal asymmetry NOT correlated to the reaction plane Many 2->2 or 2-> n processes Reduced asymmetry NOT correlated to the reaction plane final state interactions asymmetry caused not only by multiplicity fluctuations collective component is 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.

6. 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)

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

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

9. (n comp.) (5 comp.) Equations of motion (n constraints) (4 constraints) (1 constraint) closed by equation of state The limiting case of perfect fluid dynamics Wuppertal-Budapest, arXiv:1005.3508, arXiv:1007.2580 Dynamical input: -Initial conditions (uncertainty) -QCD Equation of state (from Lattice QCD) -Decoupling (uncertainty)

10. Viscous fluid dynamics Characterizes dissipative corrections in gradient expansion (4n 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.

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

12. Fluid dynamical models of heavy ion collisions

13. 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 GeV) In terms of fluid with minimal shear viscosity P. Romatschke arXiv.0902.3663

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

15. Phenomenological implication Minimal dissipation  Maximal Transparency to Fluctuations Models of the initial density distributions in AA-collisions show generically a set of event-by-event EbyE fluctuations Can we see how these spatial eccentricities propagate to asymmetries v n in momentum distributions? Fig from M.Luzum, arXiv:1107.0592 Fluctuations decay on time scale,

16. 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 2.Long-range rapidity correlation 3.Elliptic flow v 2 seems to dominate 4.Away-side peak at is smaller ( for the semi-peripheral collisions shown here ) ( implies non-vanishing odd harmonics v1, v3, … ) ( almost rapidity-independent ‘flow’ ) ATLAS prelim Flow harmonics from particle correlations @ LHC ( this is a ‘non-flow’ effect )

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

18. Flow as linear response to spatial asymmetries LHC data indicate: Spatial eccentricity is related approx. linearly to (momentum) flow Characterize spatial eccentricities, e.g., via moments of transverse density ALICE, arXiv:1105.3865, PRL

19. Hydrodynamics propagates EbyE fluctuations B. Schenke, MUSIC,.QM2012 Fluid dynamics maps initial spatial eccentricities onto measured v n 3+1 D viscous hydrodynamics with suitably chosen initial conditions reproduces v 2,v 3,v 4,v 5 in p T and centrality

20. Do smaller systems show flow: pPb? P. Bozek, 1112.0915 ATLAS, 1303.2084 A fluid dynamical simulation of pPb@LHC yields Fluid dynamics compares surprisingly well with in pPb@LHC. CMS, 1305.0609

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

22. How can non-abelian plasmas thermalize quickly? Model-dependent in QCD but a rigorously calculable problem of numerical gravity in AdS/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

23. 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)

24. End