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 Collective Flow and Mach Cones with parton transport C. Greiner HCBM workshop, Budapest, Collective Flow and Mach Cones with parton transport C. Greiner HCBM workshop, Budapest, august 2010 in collaboration with: I. Bouras, A. El, O. Fochler, F. Reining, J. Uphoff, C. Wesp, Zhe Xu - viscosity and its extraction from elliptic flow - jet quenching … same phenomena? - dissipative shocks and Mach Cones

BAMPS: Boltzmann Approach of Multi. Parton Scatterings A transport algorithm solving the Boltzmann-Equations for BAMPS: Boltzmann Approach of Multi. Parton Scatterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with p. QCD interactions (Z)MPC, VNI/BMS, AMPT new development ggg radiative „corrections“ gg, Elastic scatterings are ineffective in thermalization ! Inelastic interactions are needed ! Xiong, Shuryak, PRC 49, 2203 (1994) Dumitru, Gyulassy, PLB 494, 215 (2000) Serreau, Schiff, JHEP 0111, 039 (2001) Baier, Mueller, Schiff, Son, PLB 502, 51 (2001) BAMPS: Z. Xu and C. Greiner, PRC 71, 064901 (2005); Z. Xu and C. Greiner, PRC 76, 024911 (2007)

screened partonic interactions in leading order p. QCD elastic part radiative part J. F. screened partonic interactions in leading order p. QCD elastic part radiative part J. F. Gunion, G. F. Bertsch, PRD 25, 746(1982) T. S. Biro at el. , PRC 48, 1275 (1993) S. M. Wong, NPA 607, 442 (1996) screening mass: LPM suppression: the formation time Lg: mean free path suppressed!

Stochastic algorithm P. Danielewicz, G. F. Bertsch, Nucl. Phys. A 533, 712(1991) A. Lang Stochastic algorithm P. Danielewicz, G. F. Bertsch, Nucl. Phys. A 533, 712(1991) A. Lang et al. , J. Comp. Phys. 106, 391(1993) cell configuration in space for particles in D 3 x with momentum p 1, p 2, p 3. . . collision probability: D 3 x

Simulation: parton cascade Simulation: parton cascade

p. T spectra at collision center: x. T<1. 5 fm, Dz < 0. 4 p. T spectra at collision center: x. T<1. 5 fm, Dz < 0. 4 t fm of a central Au+Au at s 1/2=200 Ge. V Initial conditions: minijets p. T>1. 4 Ge. V; coupling as=0. 3 simulation p. QCD, only 2 -2: NO thermalization simulation p. QCD 2 -2 + 2 -3 + 3 -2 + 2 -3: thermalization! Hydrodynamic behavior!

distribution of collision angles at RHIC energies gg gg: small-angle scatterings gg ggg: large-angle distribution of collision angles at RHIC energies gg gg: small-angle scatterings gg ggg: large-angle bremsstrahlung

Shear Viscosity h Navier-Stokes approximation relation: h <-> Rtr Z. Xu and CG, Phys. Shear Viscosity h Navier-Stokes approximation relation: h <-> Rtr Z. Xu and CG, Phys. Rev. Lett. 100: 172301, 2008. Ad. S/CFT RHIC

. . . extracting viscosity Starting from a classical ansatz With the Navier-stokes approximaion . . . extracting viscosity Starting from a classical ansatz With the Navier-stokes approximaion Finally we find We find a velocity profile F. Reining

. . . extracting viscosity Green-Kubo relation: equilibrium fluctuations: C. Wesp . . . extracting viscosity Green-Kubo relation: equilibrium fluctuations: C. Wesp

Motion Is Hydrodynamic • When does thermalization occur? – Strong evidence that final state Motion Is Hydrodynamic • When does thermalization occur? – Strong evidence that final state bulk behavior reflects the initial state geometry • Because the initial azimuthal asymmetry persists in the final state dn/df ~ 1 + 2 v 2(p. T) cos (2 f) +. . . z y x 2 v 2

Elliptic Flow and Shear Viscosity in 2 -3 at RHIC 2 -3 Parton cascade Elliptic Flow and Shear Viscosity in 2 -3 at RHIC 2 -3 Parton cascade BAMPS Z. Xu, CG, H. Stöcker, PRL 101: 082302, 2008 viscous hydro. Romatschke, PRL 99, 172301, 2007 h/s at RHIC: 0. 08 -0. 2

Rapidity Dependence of v 2: Importance of 2 -3! BAMPS evolution of transverse energy Rapidity Dependence of v 2: Importance of 2 -3! BAMPS evolution of transverse energy

… looking on transverse momentum distributions gluons are not simply pions … need hadronization … looking on transverse momentum distributions gluons are not simply pions … need hadronization (and models) to understand the particle spectra

… and adding quarks as further degrees of freedom Z. Xu and C. Greiner, … and adding quarks as further degrees of freedom Z. Xu and C. Greiner, arxiv: 1001. 2912 quarks are helping in the right direction …

Relativistic Hydrodynamics Transport calculations can be used to find applicability limits of hydrodynamics To Relativistic Hydrodynamics Transport calculations can be used to find applicability limits of hydrodynamics To evaluate transport coefficients Is Israel-Stewart hydro as good as kinetic transport? ? A lot of work to do matching hydro to kinetic transport theory: Chemical equlibration is an important issue Missing terms in Israel-Stewart equations, how important are they? Even Israel – Stewart theory can lead to unphysical reheating. . .

Relativistic Hydrodynamics Add Dissipation! Second Order theory : dissipative flows are dynamic quantities W. Relativistic Hydrodynamics Add Dissipation! Second Order theory : dissipative flows are dynamic quantities W. Israel, J. Stewart 79 Causal , but. . . phenomenologic! Additional terms might be important! Need to derive hydro from kinetic theory & compare to transport results!

Precision tests: BAMPS vs Hydro in (0+1) Dim BAMPS vs Israel-Stewart Eqs. Time dependent Precision tests: BAMPS vs Hydro in (0+1) Dim BAMPS vs Israel-Stewart Eqs. Time dependent isotropic elastic cross section in BAMPS corresponds to Constant η/s in hydro A. Muronga, PRC 76 (2007) 014909 A. El, A. Muronga, Z. Xu, C. Greiner, arxiv: 0812. 2762 Israel-Stewart equations have to be corrected!

R&D for dissipative hydro > Original Israel-Stewart Equations are not ‘state of the art’ R&D for dissipative hydro > Original Israel-Stewart Equations are not ‘state of the art’ >> P. Romatschke, R. Baier et al, JHEP 0804 (2008) 100. + P. Romatschke ar. Xiv: 0902. 3663 [hep-ph]. >> B. Betz, D. Henkel, D. H. Rischke, ar. Xiv: 0812. 1440 >> G. Denicol, Xu-Guang Huang, T. Koide, D. H. Rischke, ar. Xiv: 1003. 0780 Second-order equations from kinetic theory. Israel-Stewart Eqs. do not contain all possible second-order terms! Open questions: Will additional second-order terms improve agreement between kinetic & hydro? Or rather third order? What tests can be performed? Shocks? Bjorken?

Extension of rdh to third order A. El, Z. Xu, C. Greiner, PRC 81 Extension of rdh to third order A. El, Z. Xu, C. Greiner, PRC 81 (2010) 041901 Israel-Stewart eq. a third order term For a 1 D boost invariant system: Assume, all higher order terms can be resummed to one term, Use the free-streaming solution! higher order part

Hydro vs BAMPS in 1 D A. El, Z. Xu, C. Greiner, PRC 81 Hydro vs BAMPS in 1 D A. El, Z. Xu, C. Greiner, PRC 81 (2010) 041901 x=0: Israel-Stewart x=3: third-order rel. diss. hydro x=5/3: approximative ‘all-orders’ Eq. > Resummation works at strong dissipation (large Knudsen number!) > Inclusion of third order terms reduces deviations, esp. at late times.

 gluon spectra w/o inelastic reactions A. El, A. Muronga, Z. Xu and C. gluon spectra w/o inelastic reactions A. El, A. Muronga, Z. Xu and C. Greiner, arxiv: 1007. 0705

Weak or strong …. Validity of kinetic transport - relation to shear viscosity Semiclassical Weak or strong …. Validity of kinetic transport - relation to shear viscosity Semiclassical kinetic theory? Quantum mechanics: quasiparticles?

Hard probes of the medium high energy particles are promising probes of the medium Hard probes of the medium high energy particles are promising probes of the medium created in AA-collisions n nuclear modification factor relative to pp (binary collision scaling) n QM 2008, T. Awes experiments show approx. factor 5 of suppression in hadron yields

LPM-effect n è transport model: incoherent treatment of gg ggg processes parent gluon must LPM-effect n è transport model: incoherent treatment of gg ggg processes parent gluon must not scatter during formation time of emitted gluon n discard all possible interference effects (Bethe-Heitler regime) p 1 lab frame n kt p 2 CM frame kt t = 1 / kt total boost O. Fochler

Energy Loss in a Static Medium Elastic energy loss ~T 2 ln(E / T) Energy Loss in a Static Medium Elastic energy loss ~T 2 ln(E / T) Large differential energy loss due to gg ggg Roughly d. E / dx ~ E Rapid evolution of energy spectrum E-spectrum (T = 400 Me. V, E 0 = 50 Ge. V)

Energy Loss in gg ggg Processes Cross sections ( T = 400 Me. V) Energy Loss in gg ggg Processes Cross sections ( T = 400 Me. V) Energy loss in single gg ggg Reasonable partonic cross sections over the whole energy range. Definition of the energy loss DE matters DE = Ein – max( Eiout ) DE = w

Gluon Radiation and Energy Loss Radiaton spectrum (E = 50 Ge. V) DE distribution Gluon Radiation and Energy Loss Radiaton spectrum (E = 50 Ge. V) DE distribution (E = 400 Ge. V) Heavy tail in DE distribution leads to large mean

Some BAMPS Events (CM frame) DE = 0. 67 Ge. V DE = 206. Some BAMPS Events (CM frame) DE = 0. 67 Ge. V DE = 206. 43 Ge. V DE = 26. 01 Ge. V DE = 117. 01 Ge. V

Quenching of jets first realistic 3 d results with BAMPS RAA ~ 0. 052 Quenching of jets first realistic 3 d results with BAMPS RAA ~ 0. 052 cf. S. Wicks et al. Nucl. Phys. A 784, 426 nuclear modification factor O. Fochler et al PRL 102: 202301: 2009 central (b=0 fm) Au-Au at 200 AGe. V

Non-Central RAA and High-p. T Elliptic Flow O. Fochler, Z. Xu and C. Greiner, Non-Central RAA and High-p. T Elliptic Flow O. Fochler, Z. Xu and C. Greiner, arxiv: 1003. 4380 Gluonic RAA for b = 0 and b = 7 fm Differential v 2 for b = 7 fm n n Experimental v 2 from PHENIX, ar. Xiv: 0903. 4886 inclusion of light quarks is mandatory ! … lower color factor n jet fragmentation scheme

Heavy quark elliptic flow v 2 at RHIC Jan Uphoff A. Peshier, P. B. Heavy quark elliptic flow v 2 at RHIC Jan Uphoff A. Peshier, P. B. Gossiaux, ar. Xiv: 0801. 0595 J. Aichelin, [hep-ph] Phys. Rev. C 78 (2008) PHENIX, ar. Xiv: 1005. 1627

Heavy quark RAA at RHIC PHENIX, ar. Xiv: 1005. 1627 Heavy quark RAA at RHIC PHENIX, ar. Xiv: 1005. 1627

Mach Cones in Ideal Hydrodynamics Box Simulation QCD “sonic boom” B. Betz, M. Gyulassy, Mach Cones in Ideal Hydrodynamics Box Simulation QCD “sonic boom” B. Betz, M. Gyulassy, D. Rischke, H. Stöcker, G. Torrieri

The Relativistic Riemann Problem a shock wave travels with a speed higher than speed The Relativistic Riemann Problem a shock wave travels with a speed higher than speed of sound a rarefaction wave travels to the left with the speed of sound

Riemann problem at finite viscosity I. Bouras et al, PRL 103: 032301 (2009) Tleft Riemann problem at finite viscosity I. Bouras et al, PRL 103: 032301 (2009) Tleft = 400 Me. V Tright = 200 Me. V t = 1. 0 fm/c Development of a shock plateau h/s less than 0. 1 -0. 2

time evolution of viscous shocks t=0. 5 fm/c t=1. 5 fm/c η/s = 1/(4 time evolution of viscous shocks t=0. 5 fm/c t=1. 5 fm/c η/s = 1/(4 π) t=3 fm/c Tleft = 400 Me. V Tright = 320 Me. V t=5 fm/c

Mach Cones in BAMPS Setup jet Jet has constant mean free path and only Mach Cones in BAMPS Setup jet Jet has constant mean free path and only momentum in z-direction! Medium Box scenario, no expansion of the medium, massless Boltzmann gas interactions: 2 2 with isotropic distribution of the collision angle 38

Mach Cones in BAMPS: Different Viscosities The results agree qualitatively with hydrodynamic and transport Mach Cones in BAMPS: Different Viscosities The results agree qualitatively with hydrodynamic and transport calculations → B. Betz, PRC 79: 034902, 2009 Strong collective behaviour is observed A diffusion wake is also visible, momentum flows in direction of the jet

Mach Cones in BAMPS: Different Viscosities Mach Cones in BAMPS: Different Viscosities

Mach Cones in BAMPS: Different Viscosities Mach Cones in BAMPS: Different Viscosities

Mach Cones in BAMPS: Different Viscosities The shock front (Mach front) gets broader and Mach Cones in BAMPS: Different Viscosities The shock front (Mach front) gets broader and vanish with more dissipation The viscosity smears the profile out, but does it affect the Mach angle?

Stoped Jet in BAMPS: Stoped Jet in BAMPS:

Stoped Jet in BAMPS: Stoped Jet in BAMPS:

Stoped Jet in BAMPS: Stoped Jet in BAMPS:

Stoped Jet in BAMPS: Stoped Jet in BAMPS:

Summary Inelastic/radiative p. QCD interactions (23 + 32) explain: n fast thermalization n large Summary Inelastic/radiative p. QCD interactions (23 + 32) explain: n fast thermalization n large collective flow n small shear viscosity of QCD matter at RHIC n realistic jet-quenching of gluons Future/ongoing analysis and developments: n light and heavy quarks n jet-quenching (Mach Cones, ridge) n hadronisation and afterburning (Ur. QMD) needed to determine how imperfect the QGP at RHIC and LHC can be … and dependence on initial conditions n dissipative hydrodynamics