Johann Wolfgang GoetheUniversitt Frankfurt Institut fr Theoretische Physik
- Slides: 30
Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik Microscopic Understanding of ultrarel. HIC – How dissipative is the RHIC matter ? C. Greiner, 30 th Course of Intl. School of Nuclear Physics , Erice-Sicily, september 2008 in collaboration with: I. Bouras, L. Chen, A. El, O. Fochler, J. Uphoff, Zhe Xu list of contents - fast thermalization within a p. QCD cascade - viscosity and its extraction from elliptic flow - jet quenching … same phenomena? - new: dissipative shocks
QCD thermalization using parton cascade VNI/BMS: K. Geiger and B. Müller, NPB 369, 600 (1992) S. A. Bass, B. Müller and D. K. Srivastava, PLB 551, 277(2003) ZPC: B. Zhang, Comput. Phys. Commun. 109, 193 (1998) MPC: D. Molnar and M. Gyulassy, PRC 62, 054907 (2000) AMPT: B. Zhang, C. M. Ko, B. A. Li, and Z. W. Lin, PRC 61, 067901 (2000) BAMPS: Z. Xu and C. Greiner, PRC 71, 064901 (2005); 76, 024911 (2007)
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“ 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) gg,
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
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
Initial production of partons minijets color glass condensate string matter
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 bremsstrahlung
time scale of thermalization Theoretical Result ! t = time scale of kinetic equilibration.
Transport Rates • Transport rate is the correct quantity describing kinetic equilibration. • Transport collision rates have an indirect relationship to the collision-angle distribution. Z. Xu and CG, PRC 76, 024911 (2007)
Transport Rates Large Effect of 2 -3 !
Shear Viscosity h From Navier-Stokes approximation From Boltzmann-Eq. relation between h and Rtr Z. Xu and CG, Phys. Rev. Lett. 100: 172301, 2008.
Ratio of shear viscosity to entropy density in 2<->3 RHIC Ad. S/CFT
Dissipative Hydrodynamics Shear, bulk viscosity and heat conductivity of dense QCD matter could be prime candidates for the next Particle Data Group, if they can be extracted from data. Need a causal hydrodynamical theory. What are the criteria of applicability? Causal stable hydrodynamics can be derrived from the Boltzmann Equation: -Renormalization Group Method by Kunihiro/Tsumura-->stable 1 st Order linearized BE with f=f 0+εf 1+ε²f 2 yields (2 nd Order – work in progress) can be solved by introducing projector P on Ker{A}, where A-linearized collision operator Calculate momenta of the BE. Transport coefficients and relaxation times for dissipative quantities can be calculated as functions of collision terms in BE. Andrej El -Grad‘s 14 -momentum method-->2 nd Order causal hydrodynamics. Compare dissipative relaxation times to the mean free pass from cascade simulation.
Validity of kinetic transport - relation to shear viscosity Semiclassical kinetic theory: Quantum mechanis: quasiparticle limit:
Collective Effects transverse flow velocity of local cell in the transverse plane of central rapidity bin Au+Au b=8. 6 fm using BAMPS =c
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 Z. Xu
Rapidity Dependence of v 2: Importance of 2 -3! BAMPS evolution of transverse energy
more details on elliptic flow at RHIC … moderate dependence on critical energy density h/s at RHIC: 0. 08 -0. 2
… looking on transverse momentum distributions gluons are not simply pions … need hadronization (and models) to understand the particle spectra
Quenching of jets first realistic 3 d results with BAMPS RAA ~ 0. 06 cf. S. Wicks et al. Nucl. Phys. A 784, 426 O. Fochler et al ar. Xiv: 0806. 1169 nuclear modification factor central (b=0 fm) Au-Au at 200 AGe. V
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
… possible improvements of microscopic treatment n inclusion of light quarks is mandatory ! n … lower color factor n comparison to other approaches n … LPM bremsstrahlung n jet fragmentation scheme
Mach Cones in Ideal Hydrodynamics Box Simulation Bjorken Expansion Barbara Betz, Dirk Rischke, Horst Stöcker, Giorgio Torrieri
Parton cascade meets ideal shocks: Riemann problem Tleft = 400 Me. V Tright = 200 Me. V t = 1. 0 fm/c λ = 0. 1 fm λ = 0. 001 fm I. Bouras
Tleft = 400 Me. V Tright = 320 Me. V Time evolution of viscous shocks t=0. 5 fm/c t=1. 5 fm/c η/s = 1/(4 π) t=3 fm/c t=5 fm/c
Viscous shocks Tleft = 400 Me. V - Tright = 320 Me. V , t = 3. 0 fm/c η/s ~ 0. 01 - 1. 0
Comparison to Israel-Stewart t = 1. 6 fm/c η/s = 0. 02 η/s = 0. 1 Comparison to full p. QCD transport Tleft = 400 Me. V Tright = 320 Me. V t = 3 fm/c η/s ~ 0. 1 - 0. 13
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 Thanks to the organizers for the invitation !
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