Beam energy scan using a viscous hydro+cascade model Yuriy KARPENKO Frankfurt Institute for Advanced Studies/ Bogolyubov Institute for Theoretical Physics FAIRNESS 2013, September 21, 2013 In collaboration with M. Bleicher, P . Huovinen, H. Petersen Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 1 / 18
Introduction: heavy ion collision in pictures 1 Typical size Typical lifetime 10 fm ∝ 10 − 14 m 10 fm/c ∝ 10 − 23 s 10 − 8 sec after the collision: hadrons are detected 1 Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 2 / 18
“Stages of Heavy Ion Collision” Initial(pre-thermal) stage 1 I Thermalization 1. Ingredients of hydro+cascade model : Hydrodynamic expansion 2 I Quark-gluon plasma Initial stage model 1 phase Enforced thermalization I Phase transition Hydrodynamic solution 2 I Hadron Gas phase I Equation of state for ⇔ I Chemical freeze-out hydrodynamics I End of hydrodynamic I transport coefficients regime Particlization and 3 Kinetic stage 3 switching to a cascade Kinetic freeze-out ⇓ Free streaming, then hadrons are detected Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 3 / 18
Where do we want to apply it Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 4 / 18
Where do we want to apply it small net baryon density: hydro(+cascade) model is well established arXiv: “hydrodynamic” + “RHIC” = 42 publications large net baryon density: arXiv: “hydrodynamic” + “SPS” = 8 publications arXiv: “hydrodynamic” + “FAIR” = 3 publications Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 4 / 18
1. Ingredients of the model : Initial stage: 1 UrQMD Hydrodynamic solution 2 I Equation of state for hydrodynamics: Chiral model coupled to Polyakov loop to include the deconfinement phase transition F good agreement with Ingredients essential for beam lattice QCD data at energy scan studies are µ B = 0 marked red. F Applicable also at finite baryon densities I transport coefficients EoS reference: J. Steinheimer, Particlization and 3 S. Schramm and H. Stocker, switching back to cascade J. Phys. G 38, 035001 (2011). (UrQMD) Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 5 / 18
Initial conditions for hydrodynamic evolution particle phase hydro phase incoming nuclei √ t 2 − z 2 = τ 0 (red curve): τ = T 0 µ of fluid = averaged T 0 µ of particles Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 6 / 18
Hydrodynamic stage The hydrodynamic equations in arbitrary coordinate system: ∂ ; ν T µ ν = ∂ ν T µ ν + Γ µ νλ T νλ + Γ ν νλ T µ λ = 0 (1) where (we choose Landau definition of velocity) T µ ν = ε u µ u ν − ( p + Π )( g µ ν − u µ u ν )+ π µ ν (2) and ∆ µ ν = g µ ν − u µ u ν Evolutionary equations for shear/bulk, coming from Israel-Stewart formalism: < u γ ∂ ; γ π µ ν > = − π µ ν − π µ ν − 4 3 π µ ν ∂ ; γ u γ NS (3a) τ π − 4 u γ ∂ ; γ Π = − Π − Π NS 3 Π ∂ ; γ u γ (3b) τ Π where < A µ ν > = ( 1 β + 1 β − 1 α ∆ ν 2 ∆ ν 3 ∆ µ ν ∆ αβ ) A αβ 2 ∆ µ α ∆ µ Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 7 / 18
Fluid → particle transition ε = ε sw = 0 . 5 GeV/fm 3 (end of green zone): T 0 µ of hadron-resonance gas = T 0 µ of fluid Momentum distribution from Landau/Cooper-Frye prescription: particle phase p 0 d 3 n i g i 1 Z p µ d d 3 p = ⇣ p ν u ν ( x ) − µ i ( x ) hydro phase ( 2 π ) 3 ⌘ exp ± 1 T ( x ) Cornelius subroutine ∗ is used to incoming nuclei compute ∆ σ i on transition hypersurface. UrQMD cascade is employed after particlization surface. ∗ Huovinen P and Petersen H 2012, Eur.Phys.J. A 48 171 Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 8 / 18
Model validation at top RHIC energy Setup: smooth 3D initial conditions " # − θ ( | η | − ∆ η )( | η | − ∆ η ) 2 ε ( τ 0 , ~ r T , η ) = ε MCG ( ~ r T ) · θ ( Y b − | η | ) exp σ 2 η Y b is beam rapidity, parameters: ∆ η = 1 . 3, σ η = 2 . 1 (chosen from the fit to PHOBOS dN ch / d η ) 0.18 STAR 20-30% ideal + UrQMD ideal + UrQMD 0.16 η /S=0.1 + UrQMD 2 10 η /S=0.1 + UrQMD PHENIX 20-30% 0.14 /S=0.08 + UrQMD η dy) 10 0.12 T dp 0.1 T 2 p v 1 π N/(2 0.08 2 d 0.06 10 -1 0.04 p distributions, π , K, p v all charged T -2 10 2 0.02 0 0.5 1 1.5 2 2.5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p [GeV] p [GeV] T T Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 9 / 18
Beam energy scan (BES) Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 9 / 18
Results: E lab = 158 A GeV Pb-Pb (SPS) √ s NN = 17 . 3 GeV, 0-5% central collisions ( b = 0 ... 3 . 4 fm) 200 ideal + UrQMD 180 η /S=0.1 + UrQMD /S=0.2 + UrQMD η 160 NA49 - π NA49 K+ 140 NA49 K- 120 dN/dy 100 80 60 40 20 0 -4 -2 0 2 4 y → strong viscous entropy production Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 10 / 18
Results: E lab = 158 A GeV Pb-Pb (SPS) √ s NN = 17 . 3 GeV, 0-5% central collisions ( b = 0 ... 3 . 4 fm) ideal + UrQMD η /S=0.1 + UrQMD 3 /S=0.2 + UrQMD 10 η NA49 - π NA49 K- NA49 K+ dy) 2 10 T dm T N/(m 10 2 d 1 0 0.2 0.4 0.6 0.8 1 m -m [GeV] T → viscosity causes stronger transverse expansion Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 11 / 18
Results: E lab = 158 A GeV Pb-Pb (SPS) Mid-central events as defined by NA49 ( c = 12 . 5 − 33 . 5 % ) 0.2 0.2 NA49 v {4} NA49 v {4} 2 2 0.18 0.18 NA49 v standard ideal + UrQMD 2 ideal + UrQMD η /S=0.1 + UrQMD 0.16 0.16 η /S=0.1 + UrQMD η /S=0.2 + UrQMD 0.14 0.14 η /S=0.2 + UrQMD 0.12 0.12 2 2 0.1 0.1 v v 0.08 0.08 0.06 0.06 0.04 0.04 pion v proton v 2 0.02 0.02 2 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 p [GeV] p [GeV] T T Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 12 / 18
Results: E lab = 80 , 40 , 20 A GeV Pb-Pb (SPS) Corresp. √ s NN = 12 . 3 , 8 . 8 , 6 . 3 GeV E = 80 A GeV lab ideal + UrQMD η /S=0.1 + UrQMD 3 10 η /S=0.2 + UrQMD Pion & kaon pt-distributions for NA49 π - NA49 K- dy) most central events ( c = 0 − 5 % , NA49 K+ 2 10 T dm b = 0 ... 3 . 4 fm) T N/(m 10 2 d Overall good description with η / S = 0 . 2 except for K − for lowest 1 energies 0 0.2 0.4 0.6 0.8 1 m -m [GeV] T E = 40 A GeV E = 20 A GeV lab lab ideal + UrQMD 3 ideal + UrQMD 10 3 /S=0.1 + UrQMD /S=0.1 + UrQMD η η 10 η /S=0.2 + UrQMD η /S=0.2 + UrQMD NA49 π - NA49 π - dy) NA49 K- dy) 10 2 NA49 K- 2 NA49 K+ 10 NA49 K+ T T dm dm T T N/(m N/(m 10 10 2 2 d d 1 1 -1 10 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 m -m [GeV] m -m [GeV] T T Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 13 / 18
v 2 for BES at RHIC ( √ s NN = 7 . 7 , 27 , 39 GeV Au-Au) 0.3 v {4} , s =7.7 A GeV 2 v {4} , s =27 A GeV 2 v {4} , s =39 A GeV 0.25 2 ideal + UrQMD, s =7.7 A GeV ideal + UrQMD, s =27 A GeV 0.2 ideal + UrQMD, s =39 A GeV η /S=0.2 + UrQMD, s =7.7 A GeV η /S=0.2 + UrQMD, s =27 A GeV 2 0.15 η /S=0.2 + UrQMD, s =39 A GeV v 0.1 0.05 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 p [GeV] T η / S ≥ 0 . 2 is required in hydro phase for all BES energies. Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 14 / 18
K + / π + , K − / π − vs collision energy 0.3 0.1 K+/ +, full phase space K-/ π -, full phase space π 0.09 0.25 0.08 0.07 0.2 0.06 0.15 0.05 0.04 0.1 0.03 ideal + UrQMD 0.02 η /S=0.1 + UrQMD 0.05 /S=0.2 + UrQMD η 0.01 0 0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 s [GeV] s [GeV] points: exp. data (from AGS, NA49, PHENIX) K + / π + decreases and K − / π − increases due to additional entropy production in viscous hydro phase Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 15 / 18
HBT(interferometry) measurements The only tool for space-time measurements at the scales of 10 − 15 m, 10 − 23 s ~ q = ~ p 2 − ~ p 1 k = 1 ~ 2 ( ~ p 1 + ~ p 2 ) P ( p 1 ) P ( p 2 ) = real event pairs P ( p 1 , p 2 ) C ( p 1 , p 2 ) = mixed event pairs Gaussian approximation of CFs ( q → 0): q ) = 1 + λ ( k ) e − q 2 out R 2 out − q 2 side R 2 side − q 2 long R 2 C ( ~ k , ~ long R out , R side , R long (HBT radii) correspond to homogeneity lengths , which reflect the space-time scales of emission process In an event generator, BE/FD two-particle amplitude (anti)symmetrization must be introduced Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 16 / 18
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