Beam energy scan using a viscous hydro+cascade model Yuriy KARPENKO - - PowerPoint PPT Presentation
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.
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
Typical size 10 fm ∝ 10−14m Typical lifetime 10 fm/c ∝ 10−23s 10−8sec 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”
1
Initial(pre-thermal) stage
I Thermalization 2
Hydrodynamic expansion
I Quark-gluon plasma
phase
I Phase transition I Hadron Gas phase I Chemical freeze-out I End of hydrodynamic
regime
3
Kinetic stage Kinetic freeze-out ⇓ Free streaming, then hadrons are detected ⇔
hydro+cascade model:
1
Initial stage model Enforced thermalization
2
Hydrodynamic solution
I Equation of state for
hydrodynamics
I transport coefficients 3
Particlization and switching to a cascade
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 3 / 18
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 4 / 18
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
Ingredients essential for beam energy scan studies are marked red. EoS reference: J. Steinheimer,
1
Initial stage: UrQMD
2
Hydrodynamic solution
I Equation of state for
hydrodynamics: Chiral model coupled to Polyakov loop to include the deconfinement phase transition
F good agreement with
lattice QCD data at µB = 0
F Applicable also at
finite baryon densities
I transport coefficients 3
Particlization and switching back to cascade (UrQMD)
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 5 / 18
incoming nuclei hydro phase particle phase
τ = √ t2 −z2 = τ0 (red curve): T 0µ of fluid = averaged T 0µ of particles
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 6 / 18
The hydrodynamic equations in arbitrary coordinate system: ∂;νT µν = ∂νT µν +Γµ
νλT νλ +Γν νλT µλ = 0
(1) where (we choose Landau definition of velocity) T µν = εuµuν −(p +Π)(gµν −uµuν)+πµν (2) and ∆µν = gµν −uµuν Evolutionary equations for shear/bulk, coming from Israel-Stewart formalism: < uγ∂;γπµν > = −πµν −πµν
NS
τπ − 4 3πµν∂;γuγ (3a) uγ∂;γΠ = −Π−ΠNS τΠ − 4 3Π∂;γuγ (3b) where < Aµν >= (1 2∆µ
α∆ν β + 1
2∆ν
α∆µ β − 1
3∆µν∆αβ)Aαβ
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 7 / 18
ε = εsw = 0.5 GeV/fm3 (end of green zone): T 0µ of hadron-resonance gas = T 0µ of fluid
incoming nuclei hydro phase particle phase
Momentum distribution from Landau/Cooper-Frye prescription:
p0 d3ni d3p =
Z
gi (2π)3 1 exp ⇣ pνuν(x)−µi(x)
T(x)
⌘ ±1 pµd
Cornelius subroutine∗ is used to compute ∆σi 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
Setup: smooth 3D initial conditions ε(τ0,~ rT ,η) = εMCG( ~ rT )·θ(Yb −|η|)exp " −θ(|η|−∆η)(|η|−∆η)2 σ2
η
# Yb is beam rapidity, parameters: ∆η = 1.3, ση = 2.1 (chosen from the fit to PHOBOS dNch/dη)
[GeV]
T
p
0.5 1 1.5 2 2.5
dy)
T
dp
T
p π N/(2
2
d
10
10 1 10
2
10
ideal + UrQMD /S=0.1 + UrQMD η PHENIX 20-30% , K, p π distributions,
T
p
[GeV]
T
p
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
2
v
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
STAR 20-30% ideal + UrQMD /S=0.1 + UrQMD η /S=0.08 + UrQMD η
all charged
2
v
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 9 / 18
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 9 / 18
√sNN = 17.3 GeV, 0-5% central collisions (b = 0...3.4 fm)
y
2 4 dN/dy 20 40 60 80 100 120 140 160 180 200 ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K+ NA49 K-
→ strong viscous entropy production
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 10 / 18
√sNN = 17.3 GeV, 0-5% central collisions (b = 0...3.4 fm)
T
m 0.2 0.4 0.6 0.8 1 dy)
T
dm
T
N/(m
2
d 1 10
2
10
3
10
ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K- NA49 K+
→ viscosity causes stronger transverse expansion
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 11 / 18
Mid-central events as defined by NA49 (c = 12.5−33.5%)
[GeV]
T
p
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
2
v
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
{4}
2
NA49 v standard
2
NA49 v ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
2
pion v
[GeV]
T
p
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
2
v
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
{4}
2
NA49 v ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
2
proton v
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 12 / 18
Pion & kaon pt-distributions for most central events (c = 0−5%, b = 0...3.4 fm) Overall good description with η/S = 0.2 except for K − for lowest energies
T
m
0.2 0.4 0.6 0.8 1
dy)
T
dm
T
N/(m
2
d
1 10
2
10
3
10
= 80 A GeV
lab
E ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K- NA49 K+
T
m
0.2 0.4 0.6 0.8 1
dy)
T
dm
T
N/(m
2
d
1 10
2
10
3
10
= 40 A GeV
lab
E ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K- NA49 K+
T
m
0.2 0.4 0.6 0.8 1
dy)
T
dm
T
N/(m
2
d
10 1 10
2
10
3
10
= 20 A GeV
lab
E ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K- NA49 K+ Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 13 / 18
[GeV]
T
p
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
2
v
0.05 0.1 0.15 0.2 0.25 0.3
=7.7 A GeV s , {4}
2
v =27 A GeV s , {4}
2
v =39 A GeV s , {4}
2
v =7.7 A GeV s ideal + UrQMD, =27 A GeV s ideal + UrQMD, =39 A GeV s ideal + UrQMD, =7.7 A GeV s /S=0.2 + UrQMD, η =27 A GeV s /S=0.2 + UrQMD, η =39 A GeV s /S=0.2 + UrQMD, η
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
[GeV] s
2 4 6 8 10 12 14 16 18 0.05 0.1 0.15 0.2 0.25 0.3
ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η +, full phase space π K+/
[GeV] s
2 4 6 8 10 12 14 16 18 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
π K-/
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
The only tool for space-time measurements at the scales of 10−15m, 10−23s
~ q =~ p2 −~ p1 ~ k = 1 2(~ p1 +~ p2) C(p1,p2) = P(p1,p2) P(p1)P(p2) = real event pairs mixed event pairs Gaussian approximation of CFs (q → 0): C(~ k,~ q) = 1+λ(k)e−q2
sideR2 side−q2 longR2 long
Rout,Rside,Rlong (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
Corresponding √sNN = 12.3,8.8,6.3 GeV, NA49, most central collisions (c = 0−5%)
Femtoscopic radii for π−π− pairs: Rlong,Rout consistent with NA49 data, Rside underestimated.
[GeV]
T
p
0.1 0.2 0.3 0.4 0.5 0.6
[fm]
long
R
2 3 4 5 6 7 8 = 158 A GeV
labNA49, E = 40 A GeV
labNA49, E =30 A GeV
labideal + UrQMD, E =40 A GeV
labideal + UrQMD, E =80 A GeV
labideal + UrQMD, E =158 A GeV
labideal + UrQMD, E
long
R
[GeV]
T
p
0.1 0.2 0.3 0.4 0.5 0.6
[fm]
R
3 3.5 4 4.5 5 5.5 6 6.5 7
R
[GeV]
T
p
0.1 0.2 0.3 0.4 0.5 0.6
[fm]
side
R
3 3.5 4 4.5 5 5.5 6 6.5 7 side
R
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 17 / 18
Elab = 158 A GeV SPS (√sNN = 17.3 GeV)
Dependence on η/S
[GeV]
T
p
0.1 0.2 0.3 0.4 0.5 0.6
side
/R
R
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
side
/R
R
[GeV]
T
p
0.1 0.2 0.3 0.4 0.5 0.6
[fm]
long
R
2 3 4 5 6 7 8
=158 A GeV
lab
NA49, E ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η long
R
Rlong is increased and Rout/Rside is slightly improved by viscosity
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
Viscous hydro + UrQMD model: 3+1D viscous hydrodynamics EoS at finite µB (Chiral model) Conclusions: model validated at top RHIC energy, and applied for BES. shear viscosity in hydro phase improves description of
I pT -spectra I dN/dy I elliptic flow I femtoscopic radii
v2 from RHIC BES suggests η/S ≥ 0.2
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
Viscous hydro + UrQMD model: 3+1D viscous hydrodynamics EoS at finite µB (Chiral model) Conclusions: model validated at top RHIC energy, and applied for BES. shear viscosity in hydro phase improves description of
I pT -spectra I dN/dy I elliptic flow I femtoscopic radii
v2 from RHIC BES suggests η/S ≥ 0.2 Thank you for your attention!
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
The hydrodynamic equations in arbitrary coordinate system: ∂;νT µν = ∂νT µν +Γµ
νλT νλ +Γν νλT µλ = 0
(4) where (we choose Landau definition of velocity) T µν = εuµuν −(p +Π)(gµν −uµuν)+πµν (5) and ∆µν = gµν −uµuν Evolutionary equations for shear/bulk, coming from Israel-Stewart formalism: < uγ∂;γπµν > = −πµν −πµν
NS
τπ − 4 3πµν∂;γuγ (6a) uγ∂;γΠ = −Π−ΠNS τΠ − 4 3Π∂;γuγ (6b) where < Aµν >= (1 2∆µ
α∆ν β + 1
2∆ν
α∆µ β − 1
3∆µν∆αβ)Aαβ
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
Typical smooth (event-averaged) initial condition for Elab = 168 A GeV midcentral SPS collisions. energy density [GeV/fm3] distribution:
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
Typical smooth (event-averaged) initial condition for Elab = 168 A GeV midcentral SPS collisions. vη distribution (notice nonzero angular momentum!):
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
η/S = 0
[GeV]
T
p 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
2
v 0.05 0.1 0.15 0.2 0.25 =7.7 GeV s model, full =7.7 GeV s model, hydro only =39 GeV s model, full =39 GeV s model, hydro only
full vs hydro_only
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
hydro→cascade transition
Most central collisions,
Elab =20 GeV (cyan)...158 GeV (red) √sNN = 6.27...17.3 GeV Transition criterion: ε = εcrit = 0.5 GeV/fm3, same for all energies
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 τ [fm/c] ry [fm] E=158 A GeV E=80 A GeV E=40 A GeV E=30 A GeV E=20 A GeV 1 2 3 4 5 6 7 8 9
0.5 1 1.5 τ [fm/c] η
System squeezes in rapidity with decreasing collision energy, hydro phase still lasts about 4.5 fm/c at lowest SPS energy.
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
Procedure (for each surface element): {ε = εcrit,nB,nQ} EoS − − → {T,µB,µQ,µS} Most central collisions,
Elab =20 GeV (cyan)...158 GeV (red)
T(rapidity) (top), T(τ) (bottom left), µB(τ) (bottom right)
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
protons & antiprotons most central events (b = 0..3.4 fm)
y
1 2 3 4 /dy
net protons
dN 5 10 15 20 25 30 35 40 45 50
the model, ideal /S=0.1 η the model, /S=0.2 η the model,
net protons
T
m 0.2 0.4 0.6 0.8 1 1.2 dy)
T
dm
T
N/(m
2
d
10 1 10
2
10
NA49, 158GeV, p p NA49, 158GeV,
Hydrodynamic τstart = 1.42 fm/c
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
pions & kaons most central events (b = 0..3.4 fm)
y
1 2 3 4 dN/dy 20 40 60 80 100 120
the model, ideal /S=0.1 η the model, /S=0.2 η the model,
NA49, 40GeV NA49, 40GeV, K+ NA49, 40GeV, K-
T
m
0.2 0.4 0.6 0.8 1
dy)
T
dm
T
N/(m
2
d
1 10
2
10
3
10
= 40 A GeV
lab
E ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K- NA49 K+
Hydrodynamic τstart = 2.83 fm/c
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
protons & antiprotons most central events (b = 0..3.4 fm)
y
1 2 3 /dy
net protons
dN 5 10 15 20 25 30 35 40 45 50
the model, ideal /S=0.1 η the model, /S=0.2 η the model,
net protons
T
m 0.2 0.4 0.6 0.8 1 1.2 1.4 dy)
T
dm
T
N/(m
2
d
10
10 1 10
2
10
NA49, 40 GeV, p p NA49, 40 GeV,
Hydrodynamic τstart = 2.83 fm/c
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
pions & kaons most central events (b = 0..3.4 fm)
y
2 4 dN/dy 20 40 60 80 100
the model, ideal /S=0.1 η the model, /S=0.2 η the model,
NA49, NA49, K+ NA49, K-
T
m 0.2 0.4 0.6 0.8 1 dy)
T
dm
T
N/(m
2
d
10 1 10
2
10
3
10 the model, sps30 ideal /S=0.1 η the model, sps30 /S=0.2 η the model, sps30
NA49, 30GeV, + π NA49, 30GeV, NA49, 30GeV, K- NA49, 30GeV, K+
Hydrodynamic τstart = 3.28 fm/c
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18
pions & kaons most central events (b = 0..3.4 fm)
y
1 2 3 4 dN/dy 10 20 30 40 50 60 70 80 90
the model, ideal /S=0.1 η the model, /S=0.2 η the model,
NA49, NA49, K+ NA49, K-
T
m
0.2 0.4 0.6 0.8 1
dy)
T
dm
T
N/(m
2
d
10 1 10
2
10
3
10
= 20 A GeV
lab
E ideal + UrQMD /S=0.1 + UrQMD η /S=0.2 + UrQMD η
NA49 NA49 K- NA49 K+
Hydrodynamic τstart = 4.05 fm/c
Yuriy Karpenko (FIAS/BITP) Energy scan using visc.hydro+cascade FAIRNESS 2013, September 21, 2013 18 / 18