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Flow in heavy ion collisions

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 with momentum p. b.

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Flow in heavy ion collisions

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  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 with momentum p b Particle production w.r.t. reaction plane 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: Borghini, Dinh, Ollitrault, PRC (2001) This requires signals

  7. Reaction plane • Momentum space v2 @ LHC • Signal implies 2-1 asymmetry of particles production w.r.t. reaction plane. • ‘Non-flow’ effect for 2nd order cumulants pT-integrated v2 2nd order cumulants do not characterize solely collectivity. Strong Collectivity !

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

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

  10. Characterizes dissipative corrections in gradient expansion Viscous fluid dynamics (4n comp.) (10 comp.) To close equation of motion, supplement conservation laws and eos (n constraints) (1 constraint) (4 constraints) by point-wise validity of 2nd 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. Fluid-dynamic evolution: governs dominant dissipative mode Sound attenuation length final Pics by B. Schenke initial Decoupling: e.g. on space-time hypersurface , defined by, possibly followed by hadronic rescattering Cooper- Frye freeze-out

  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 P. Romatschke arXiv.0902.3663 • 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

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

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

  16. 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: • Small-angle jet-like correlations around • Long-range rapidity correlation • Elliptic flow v2 seems to dominate • Away-side peak at is smaller (this is a ‘non-flow’ effect) ATLAS prelim (almost rapidity-independent ‘flow’) (for the semi-peripheral collisions shown here) (implies non-vanishing odd harmonics v1, v3, …)

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

  19. Hydrodynamics propagates EbyE fluctuations • Fluid dynamics maps initial spatial eccentricities onto measured vn • 3+1 D viscous hydrodynamics • with suitably chosen initial conditions • reproduces v2,v3,v4,v5 in pT and centrality B. Schenke, MUSIC, .QM2012

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

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

  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)

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