Quantifying the properties of Hot QCD Matter – INT Seattle, July 2010 Anisotropies in momentum space in a Transport Approach V. Greco UNIVERSITY of CATANIA INFN-LNS Quantifying the properties of Hot QCD Matter – INT Seattle, July 2010

Information from non-equilibrium: Elliptic Flow px py x y z v2/e measures the efficiency of the convertion of the anisotropy from Coordinate to Momentum space Fourier expansion in p-space l=(sr)-1 | viscosity c2s=dP/de | EoS c2s= 1/3 Parton Cascade 2v2/e time c2s= 0.6 c2s= 0.1 Measure of P gradients Hydrodynamics l=0 Massless gas e=3P -> c2s=1/3 More generally one can distinguish: Short range: collisions -> viscosity Long range: field interaction -> e ≠ 3P D. Molnar & M. Gyulassy, NPA 697 (02) Bhalerao et al., PLB627(2005)

First stage of RHIC Parton cascade Hydrodynamics + EoS P(e) Parton elastic 22 interactions (l=1/sr - P=e/3) No microscopic details (mean free path  -> 0, h=0) + EoS P(e) v2 saturation pattern reproduced

At RHIC a finite v4 observed If v2 is very large More harmonics needed to describe an elliptic deformation -> v4 To balance the minimum v4 >0 require v4 ~ 4.4% if v2= 25% At RHIC a finite v4 observed for the first time !

Outline Results from RHIC Cascade 2<->2 collisions at fixed h/s: bulk, jets, hadronization, heavy quarks -> motivation for a transport approach Cascade 2<->2 collisions at fixed h/s: Scaling properties of v2(pT)/ex Link v2(pT) - h/s~0.1-0.2 and coalescence Large v4/(v2)2 Transport Theory with Mean Field at fixed h/s: NJL chiral phase transition and v2 <-> h/s Extension to quasiparticle models fitted to lQCD e,P

From the State of the Art -> Transport Initial Conditions Quark-Gluon Plasma Hadronization BULK (pT~T) Microscopic Mechanism Matters! CGC (x<<1) Gluon saturation MINIJETS (pT>>T,LQCD) Heavy Quarks (mq>>T,LQCD) From RHIC but more relevant at LHC: Initial Condition – “exotic” non equilibrium Bulk – Hydrodynamics BUT large finite viscosities (h,z) Minijets – perturbative QCD BUT strong Jet-Bulk “talk” Heavy Quarks – Brownian particle (?) BUT strongly coupled to Bulk Hadronization – Microscopic mechanism can modify QGP observables Non-equilibrium + microscopic scale are relevant in all the subfields A unified framework against a separate modelling can be useful

Viscous Hydrodynamics Relativistic Navier-Stokes (Hooke law like) but it violates causality, II0 order expansion needed -> Israel-Stewart tensor based on entropy increase ∂m sm >0 - th,tz two parameters appears - df (pT) quite arbitrary - df~ feq reduce the pT validity range P. Romatschke, PRL99 (07)

Transport approach Discriminate short and long range interaction: Field Interaction -> e≠3P Free streaming Collisions -> h≠0 C23 better not to show… Discriminate short and long range interaction: Collisions (l≠0) + Medium Interaction ( Ex. Chiral symmetry breaking) r,T decrease

Motivation for Transport approach Wider Range of validity in h, z, pT + microscopic level -> hadronization l->0 Hydrodynamic limit can be derived It is a 3+1D (viscous hydro 2+1D till now) No gradient expansion, full calculation valid also at intermediate pT - out of equilibrium region of the modified hadronization at RHIC valid at high h/s -> LHC include hadronization by coalescence+fragmentation CGC pT out of equilibrium impact (beyond the difference in ex) not possibile in hydrodynamics naturally including Bulk viscosity z

Transport ->Cascade approach Solved discretizing the space in (h, x, y)a cells Collision integral not solved with the geometrical interpretation, but with a local stochastic sampling Z. Xhu, C. Greiner, PRC71(04) t0 3x0 exact solutions of the Boltzmann equation D3x Questions that we want to address: What scalings survive for a fluid at finite h/s? Can we constrain /s by v2? Are both v2(pT) and v4 (pT) consistent with a unique h/s? Are v2(pT) and v4 (pT) at finite h/s consistent with Quark Number Scaling?

We simulate a constant shear viscosity Relativistic Kinetic theory Cascade code (*) =cell index in the r-space =cell index in the r-space Time-Space dependent cross section evaluated locally The viscosity is kept constant varying s (different from D. Molnar arXiV:0806.0026 P. Huovinen-D. Molnar, PRC79 (2009)) A rough estimate of (T) Neglecting  and inserting in (*) At T=200 MeV tr10 mb G. Ferini et al., PLB670 (09) V. Greco at al., PPNP 62 (09)

Analizing the scaling of v2(pT)/ex Is the finite h/s that causes the breaking of v2/e scaling? The v2 /<v2> scaling validates the ideal hydrodynamics?

Relation between ex and v2 in Hydro Bhalerao et al., PLB627(2005) STAR, PRC77(08) Hydrodynamics 2v2/e time Ideal Hydrodynamics (no size scale): v2/e scales with : - impact parameter - system size Does the breaking come from finite h/s?

Parton Cascade – without a freeze-out v2/ and v2/<v2> as a function of pT Au+Au & Cu+Cu@200 AGeV 4p/s=1 Scaling for both v2/<v2> and v2/ for both Au+Au and Cu+Cu Agreement with PHENIX data for v2/<v2> /s1/4 on top to data, but… this is missleading

Freeze-out is crucial ! Experimentally… PHENIX PRL 98, 162301 (2007) v2(pT)/ does not scale! v2(pT)/<v2> scales! PHENIX PRL 98, 162301 (2007) Note: Scaling also outside the pT hydro region STAR, PRC77 (2008) Can a cascade approach account for this? Freeze-out is crucial !

At 4ph/s ~ 8 viscous hydrodynamics is not applicable! Two kinetic freeze-out scheme Finite lifetime for the QGP small h/s fluid! collisions switched off for <c=0.7 GeV/fm3 b) /s increases in the cross-over region, faking the smooth transition between the QGP and the hadronic phase No f.o. At 4ph/s ~ 8 viscous hydrodynamics is not applicable!

Results with both freeze-out and no freeze-out No f.o. No f.o. Au+Au@200 AGeV v2/ scaling broken v2/<v2> scaling kept! Cascade at finite h/s + freeze-out : V2/ broken in a way similar to STAR data Agreement with PHENIX and STAR scaling of v2/<v2> Freeze-out + h/s lowers the v2(pT) at higher pT …

Short Reminder from coalescence… Enhancement of v2 Quark Number Scaling Molnar and Voloshin, PRL91 (03) Fries-Nonaka-Muller-Bass, PRC68(03) v2 for baryon is larger and saturates at higher pT v2q fitted from v2p GKL, PRC68(03) Is it reasonable the v2q ~0.08 needed by Coalescence scaling ? Is it compatible with a fluid h/s ~ 0.1-0.2 ? Greco-Ko-Levai,PRC68(03)

Role of Reco for h/s estimate Parton Cascade at fixed shear viscosity Hadronic h/s included -> shape for v2(pT) consistent with that needed by coalescence A quantitative estimate needs an EoS with e≠ 3P : vs2(T) < 1/3 -> v2 suppression ~ 30% -> h/s ~ 0.1 may be in agreement with coalesccence Agreement with Hydro at low pT 4/s >3  too low v2(pT) at pT1.5 GeV/c even with coalescence 4/s =1 not small enough to get the large v2(pT) at pT2 GeV/c without coalescence

Uncertain hadronic h/s Effect of h/s of the hadronic phase Hydro evolution at h/s(QGP) down to thermal f.o. -> ~50% Error in the evaluation of h/s Uncertain hadronic h/s is less relevant

Effect of h/s of the hadronic phase at LHC Pb+Pb @ 5.5 ATeV , b= 8 fm |y|<1 The mixed phase becomes irrelevant!

What about v4 ? Relevance of time scale ! v4 more sensitive to both h/s and f.o. v4(pT) at 4ph/s=1-2 could also be consistent with coalescence v4 generated later than v2 : more sensitive to properties at TTc

Very Large v4/(v2)2 ratio Ratio v4/v22 not very much depending on h/s Same Hydro with the good dN/dpT and v2 Ratio v4/v22 not very much depending on h/s and not on the initial eccentricity and not on particle species and not on impact parmeter… See M. Luzum, C. Gombeaud, O. Ollitrault, arxiv:1004.2024

Effect of h/s(T) on the anisotropies 4ph/s 1 T/Tc QGP 2 V2 develops earlier at higher h/s V4 develops later at lower h/s -> v4/(v2)2 larger v4/(v2)2 ~ 0.8 signature of h/s close to phase transition! Au+Au@200AGeV-b=8fm |y|<1 Hydrodynamics Effect of finite h/s+f.o. Effect of h/s(T) + f.o.

At LHC v4/(v2)2 large time scale … Pb+Pb @ 5.5 ATeV , b= 8 fm |y|<1 4ph/s=1 4ph/s=1 + f.o. 4ph/s(T) + f.o. Only RHIC has the right time scale to infere the T dependence of h/s!

Impact of the Mean Field and/or of the Chiral phase transition - From Cascade to Boltzmann-Vlasov Transport - Impact of an NJL mean field dynamics - Toward a transport calculation with a lQCD-EoS

NJL Mean Field Two effects: free gas scalar field interaction Associated Gap Equation Two effects: - e ≠ 3p no longer a massless free gas, cs <1/3 - Chiral phase transition Fodor, JETP(2006) NJL gas

Boltzmann-Vlasov equation for the NJL Self-Consistently derived from NJL lagrangian Mass generation affects momenta -> attractive contribution Contribution of the NJL mean field Simulating a constant h/s with a NJL mean field Massive gas in relaxation time approximation =cell index in the r-space M=0 The viscosity is kept modifying locally the cross-section

Dynamical evolution with NJL Au+Au @ 200 AGeV for central collision, b=0 fm.

Does the NJL chiral phase transition affect the elliptic flow of a fluid at fixed h/s? S. Plumari et al., PLB689(2010) NJL mean field reduce the v2 : attractive field If h/s is fixed effect of NJL compensated by cross section increase v2 <-> h/s not modified by NJL mean field dynamics Extension to realistic EoS -> quasiparticle model fitted to lQCD

Next step - use a quasiparticle model with a realistic EoS [vs(T)] for a quantitative estimate of h/s to compare with Hydro… but still missing the 3-body collisions and also hadronization…

° A. Bazavov et al. 0903.4379 hep-lat Using the QP-model of Heinz-Levai U.Heinz and P. Levai, PRC (1998) WB=0 guarantees Thermodynamicaly consistency M(T), B(T) fitted to lQCD [A. Bazavov et al. 0903.4379 ]data on e and P e NJL P QP lQCD-Fodor ° A. Bazavov et al. 0903.4379 hep-lat

Summary Transport at finite h/s+ f.o. can pave the way for a consistency among known v2,4 properties: breaking of v2(pT)/ & persistence of v2(pT)/<v2> scaling Large v4/(v2)2 ratio signature of h/s(T) (at RHIC) v2(pT), v4(pT) at h/s~0.1-0.2 can agrees with what needed by coalescence (QNS) NJL chiral phase transition do not modify v2 <-> h/s Next Steps : Include the effect of an EoS fitted to lQCD Implement a Coalescence + Fragmentation mechanism

Simulating a constant h/s with a NJL mean field Massive gas in relaxation time approximation =cell index in the r-space M=0 The viscosity is kept modifying locally the cross-section Theory Code s =10 mb

Picking-up four main results at RHIC Nearly Perfect Fluid, Large Collective Flows: Hydrodynamics good describes dN/dpT + v2(pT) with mass ordering BUT VISCOSITY EFFECTS SIGNIFICANT High Opacity, Strong Jet-quenching: RAA(pT) <<1 flat in pT - Angular correlation triggered by jets pt<4 GeV STRONG BULK-JET TALK: Hydro+Jet model non applicable at pt<8-10 GeV Hadronization modified, Coalescence: B/M anomalous ratio + v2(pT) quark number scaling (QNS) MICROSCOPIC MECHANISM: NO Hydro+Statistical hadronization Heavy quarks strongly interacting: small RAA large v2 (hard to get both) pQCD fails: large scattering rates NO BROWNIAN MOTION, NO FULL THERMALIZATION ->Transport Regime

Test in a Box at equilibrium Calculation for Au+Au running …

Boltzmann-Vlasov equation for the NJL Numerical solution with d-function test particles Contribution of the NJL mean field Test in a Box with equilibrium f distribution