Dynamics of hot dense QCD matter from RHIC

Dynamics of hot & dense QCD matter: from RHIC to LHC Steffen A. Bass Duke University • RHIC: the emerging picture • Modeling of Relativistic Heavy-Ion Collisions • Relativistic Fluid Dynamics • Hybrid Macro+Micro Transport • Model Validation: RHIC • Predictions for LHC • Spectra & Yields • Collective Flow • Transport Coefficients: Low Viscosity Matter at LHC? Steffen A. Bass collaborators: • J. Ruppert • T. Renk • C. Nonaka • B. Mueller • A. Majumder • M. Asakawa 1

RHIC: the emerging picture Steffen A. Bass 2

Exploring QCD Matter at RHIC and LHC hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization Lattice-Gauge Theory: • rigorous calculation of QCD quantities • works in the infinite size / equilibrium limit Experiments: • observe the final state + penetrating probes • rely on QGP signatures predicted by Theory Phenomenology & Transport Theory: • connect QGP state to observables • provide link between LGT and data Steffen A. Bass 3

Current Picture of QGP Structure: - Lessons from RHIC Jet-Qenching & Elliptic Flow: • QGP produced at RHIC has very large opacity • behaves like an ideal fluid (vanishing viscosity) Lattice Gauge Theory & Parton Recombination: • at TC, QGP degrees of freedom carry the quantum numbers of quarks and recombine to form hadrons Applicability of Ideal Fluid Dynamics and Statistical Model: • matter produced is thermalized • thermalization (isotropization) occurs very early, ~0. 6 fm/c Steffen A. Bass 4

Modeling of Relativistic Heavy-Ion Collisions Steffen A. Bass 5

Survey of Transport Approaches Steffen A. Bass 6

Relativistic Fluid Dynamics Steffen A. Bass 7

Relativistic Fluid Dynamics • transport of macroscopic degrees of freedom • based on conservation laws: μTμν=0 μjμ=0 • for ideal fluid: Tμν= (ε+p) uμ uν - p gμν and jiμ = ρi uμ • Equation of State needed to close system of PDE’s: p=p(T, ρi) Ø connection to Lattice QCD calculation of Eo. S • initial conditions (i. e. thermalized QGP) required for calculation • assumes local thermal equilibrium, vanishing mean free path Ø applicability of hydro is a strong signature for a thermalized system Steffen A. Bass 8

3 D-Hydro: Validation at RHIC separate chemical f. o. simulated by rescaling p, K • 1 st attempt to address all data w/ 1 calculation Nonaka & Bass: PRC 75, 014902 (2007) See also Hirano; Kodama et al. b=6. 3 fm Steffen A. Bass 9

Ideal RFD: Challenges • centrality systematics of v 2 less than perfect • no flavor dependence of cross-sections • separation chemical and kinetic freeze-out: • normalize spectra by hand • PCE: proper normalization, wrong v 2 Nu Xu Viscosity: Csernai QGP: Arnold, Moore & Yaffe HG: Prakash et al. Steffen A. Bass • success of ideal RFD argues for a low viscosity in QGP phase Ø compatible with Ad. S/CFT bound of 1/4π • viscosity will stongly change as function of temperature during collision Ø need to account for viscous corrections in hadronic phase 10

Hybrid Hydro+Micro Approaches Steffen A. Bass 11

3 D-Hydro + Ur. QMD Model Full 3 -d Hydrodynamics QGP evolution Hadronization Cooper-Frye formula Ur. QMD hadronic rescattering Monte Carlo TC TSW t fm/c + micro. transport (Ur. QMD) Hydrodynamics • • • ideally suited for dense systems – model early QGP reaction stage well defined Equation of State parameters: – initial conditions – Equation of State Bass & Dumitru, PRC 61, 064909(2000) Teaney et al, nucl-th/0110037 Nonaka & Bass, PRC 75, 014902 (2007) Hirano et al. nucl-th/0511046 Steffen A. Bass • no equilibrium assumptions Ø model break-up stage Ø calculate freeze-out Ø includes viscosity in hadronic phase • parameters: – (total/partial) cross sections matching condition: • use same set of hadronic states for Eo. S as in Ur. QMD • generate hadrons in each cell using local T and μB 12

3 D-Hydro+Ur. QMD: Validation Ø good description of cross section dependent features & nonequilibrium features of hadronic phase Ø hydrodynamic evolution used for calculation of hard probes Steffen A. Bass 13

Predictions for LHC Steffen A. Bass 14

Initial Conditions @ LHC Ørequired for all hydro-based calculations • can be obtained from: § ab-inito calculations of initial state § analysis of LHC data § phenomenological extrapolation of RHIC data PHOBOS extrapolation: • extend longitudinal scaling • self-similar trapezoidal shape U. Wiedemann QM 06 Saturation model scaling: • ASW: d. Nch/d =1650 • KLN: d. Nch/d =1800 -2100 • EHNRR: d. Nch/d =2570 Steffen A. Bass 15

3 D-Hydro+Ur. QMD: Initial Conditions • Initial Conditions: – energy density longitudinal profile transverse plane – baryon number density – parameters: 0, max , n. Bmax, 0, – flow profile: v. L= Bjorken’s solution); v. T=0 • Equation of State – 1 st order phase transition – Tc=160 Me. V • switching temperature – TSW=150 Me. V RHIC LHC-Bj LHC-1 LHC-2 0(fm) 0. 6 0. 3 0. 2 0 (Ge. V/fm 3) 55 230 1000 500 0 0. 5 N/A 1. 0 1. 4 N/A 6. 0 • note that LHC-Bj initial conditions were not meant to provide a reasonable guess for LHC but rather elucidate a scenario more extreme than RHIC Steffen A. Bass 16

Spectra & Yields Disclaimer: • do not take the following “predictions” too seriously • they only represent placeholders to demonstrate the capabilities of this particular transport approach • once data are available, the parameters of the initial condition will be adjusted in order to establish whether 3 D-Hydro+Ur. QMD can provide a viable description of QGP dynamics at LHC Steffen A. Bass 17

Blast from the Past: Bj-Hydro+Ur. QMD SAB & A. Dumitru: Phys. Rev. C 61 064909 (2000): • boost-invariant 1+1 D RFD with Ur. QMD as hadronic afterburner • RFD validated with SPS data [Dumitru & Rischke: PRC 59 354 (1999)] Ødynamic transition from QGP & mixed phase to hadronic phase • increase in <pt> as function of hadron mass less than linear due to flavordependence of hadronic rescattering Steffen A. Bass 18

From SPS to LHC • from RHIC to LHC: lifetime of QGP phase nearly doubles • only 33% increase in collision numbers of hadronic phase Steffen A. Bass 19

3 D-Hydro+Ur. QMD: Multiplicities d. N/dy LHC-1 LHC-2 at y. CM Steffen A. Bass + 1715 904 K+ 228 123 p 57 34 0+ 0 33 19 + 4. 3 2. 5 - 0. 85 0. 52 20

3 D-Hydro+Ur. QMD: Spectra Steffen A. Bass 21

3 D-Hydro+Ur. QMD: dissipative effects • hadronic phase “cools” pion spectrum • built-up of radial flow for heavier particles Ø pion wind • significant dissipative effects Ø early chemical freeze-out manifest in proton distribution (pure Hydro would need PCE) Steffen A. Bass 22

Hybrid RFD+Boltzmann Summary • validated at RHIC for soft sector and jet energy-loss • treatment of viscosity in hadronic phase • separation of thermal & chemical freeze-out Ø allows for consistent treatment of bulk matter dynamics and hard probes Steffen A. Bass 23

Collective Flow Steffen A. Bass 24

Collision Geometry: Elliptic Flow Reaction plane z Ø The applicability of fluid-dynamics suggests that the medium is in local thermal equilibrium! Ø Note that fluid-dynamics cannot make any statements how the medium reached the equilibrium stage… y x elliptic flow (v 2): • gradients of almond-shape surface will lead to preferential emission in the reaction plane • asymmetry out- vs. in-plane emission is quantified by 2 nd Fourier coefficient of angular distribution: v 2 Ø calculable with fluid-dynamics Steffen A. Bass 25

Elliptic flow: early creation P. Kolb, J. Sollfrank and U. Heinz, PRC 62 (2000) 054909 time evolution of the energy density: initial energy density distribution: spatial eccentricity momentum anisotropy Most hydro calculations suggest that flow anisotropies are generated at the earliest stages of the expansion, on a timescale of ~ 5 fm/c if a QGP Eo. S is assumed. Steffen A. Bass 26

3 D-Hydro (+Ur. QMD): Elliptic Flow • no significant sensitivity to the two initial conditions ( note Kolb, Sollfrank & Heinz: PLB 459 (1999) 667: only small rise) • dissipative effects in hadronic phase do not affect built-up of elliptic flow Ø robust early time signal Steffen A. Bass 27

Transport Coefficients: Low Viscosity Matter M. Asakawa, S. A. Bass & B. Mueller: Phys. Rev. Lett. 96 (2006) 252301 Prog. Theo. Phys. 116 (2006) 725 Steffen A. Bass 28

Viscosity: from RHIC to LHC initial state hadronic phase and freeze-out QGP and hydrodynamic expansion pre-equilibrium hadronization large elliptic flow & success of ideal RFD: zero/small viscosity expanding hadron gas w/ significant & increasing mean free path: large viscosity • viscosity of matter changes strongly with time & phase • Hydro+Ur. QMD: viscous corrections for hadron gas phase • how to understand low viscosity in QGP phase? • will low viscosity features persist at LHC? Steffen A. Bass 29

The s. QGP Dilemma Ø the success of ideal hydrodynamics has led the community to equate low viscosity with a vanishing mean free path and thus large parton cross sections: strongly interacting QGP (s. QGP) • microscopic transport theory shows that assuming quasi-particle q & g degrees of freedom would require unphysically large parton cross sections to match elliptic flow data • even for λ 0. 1 fm (close to uncertainty bound) dissipative effects are large D. Molnar Ø does a small viscosity have to imply that matter is strongly interacting? Ø consider effects of (turbulent) color fields Steffen A. Bass 30

Anomalous Viscosity: Ø any contribution to the shear viscosity not explicitly resulting from momentum transport via a transport cross section • Plasma physics: – A. V. = large viscosity induced in nearly collisionless plasmas by long-range fields generated by plasma instabilities. • Astrophysics - dynamics of accretion disks: – A. V. = large viscosity induced in weakly magnetized, ionized stellar accretion disks by orbital instabilities. • Biophysics: – A. V. = The viscous behavior of nonhomogenous fluids, e. g. , blood, in which the apparent viscosity increases as flow or shear rate decreases toward zero. • Can the QGP viscosity be anomalous? – Expanding plasmas (e. g. QGP @ RHIC) have anisotropic momentum distributions – plasma turbulence arises naturally in plasmas with an anisotropic momentum distribution (Weibel-type instabilities). Ø soft color fields generate anomalous transport coefficients, which may give the medium the character of a nearly perfect fluid even at moderately weak coupling. Steffen A. Bass 31

Weibel (two-stream) instability Ultra-Relativistic Heavy-Ion Collision: two streams of colliding color charges • consider the effect of a seed magnetic field with • pos. charges deflect as shown: alternately focus and defocus • neg. charges defocus where pos. focus and vice versa Ø net-current induced, grows with time • induced current creates B, adds to seed B • opposing currents repel each other: filamentation Ø exponential Weibel instability Guy Moore, Mc. Gill Univ. Steffen A. Bass 32

Hard Thermal Loops: Instabilities Nonabelian Vlasov equations describe interaction of “hard” (i. e. particle) and “soft” color field modes and generate the “hard-thermal loop” effective theory: Effective HTL theory permits systematic study of instabilities of “soft” color fields: find HTL modes for anisotropic distribution: Ø for any ξ 0 there exist unstable modes Ø energy-density and growth rate of unstable modes can be calculated: Romatschke & Strickland, PRD 68: 036004 (2003) Arnold, Lenaghan & Moore, JHEP 0308, 002 (2003) Mrowczynski, PLB 314, 118 (1993) Steffen A. Bass 33

Anomalous Viscosity Derivation: Sketch • linear Response: connect η with momentum anisotropy Δ: • use color Vlasov-Boltzmann Eqn. to solve for f and Δ: • Turbulent color field assumption: • ensemble average over fields: Ø diffusive Vlasov-Boltzmann Eqn: • example: anomalous viscosity in case of transverse magnetic fields • complete calculation of η via variational principle: Steffen A. Bass 34

Collisional vs. Anomalous Viscosity collisional viscosity: • derived in HTL weak coupling limit anomalous viscosity: • induced by turbulent color fields, due to momentum-space anisotropy • with ansatz for fields: Ø for reasonable values of g: A < C Steffen A. Bass M. Asakawa, S. A. Bass & B. Mueller: Phys. Rev. Lett. 96 (2006) 252301 Prog. Theo. Phys. 116 (2006) 725 35

Time-Evolution of Viscosity hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium viscosity: • relaxation rates are additive Ø sumrule for viscosities: hadronization ? ? Ø smaller viscosity dominates in system w/ 2 viscosities! temperature evolution: Steffen A. Bass 36

Viscosity at LHC: Two Scenarios field picture: • (turbulent) color fields induce an anomalous viscosity, which keeps the total shear-viscosity small during the QGP evolution Ø perfect liquidity in the weak coupling limit collisional picture: • weaker coupling at LHC vs. RHIC will lead to a larger viscosity Ø increase in dissipative effects, deviations from ideal fluid Ø elliptic flow at LHC compared to RHIC can act as a decisive measurement for the dominance of anomalous viscosity Steffen A. Bass 37

Summary and Outlook • Heavy-Ion collisions at RHIC have produced a state of matter which behaves similar to an ideal fluid Ø Hydro+Micro transport approaches are the best tool to describe the soft, non-perturbative physics at RHIC after QGP formation Ø at LHC, such hybrid models should perform well if QGP matter is found to have a low viscosity • a small viscosity does not necessarily imply strongly interacting matter! Ø (turbulent) color fields induce an anomalous viscosity, which keeps the total sheer-viscosity small during the QGP evolution Ø elliptic flow at LHC as decisive measurement on impact of anomalous viscosity Note: • due to it’s slow & nearly isotropic expansion, the early Universe most likely did not have an anomalous contribution to its viscosity Steffen A. Bass 38

The End Steffen A. Bass 39

Elliptic Flow: ultra-cold Fermi-Gas • Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultrarelativistic heavy-ion collisions Ø Elliptic flow is a general feature of strongly interacting systems! Steffen A. Bass 40