Transcript Partial thermalization, a key ingredient of the HBT Puzzle

Partial thermalization,
a key ingredient
of the HBT Puzzle
Clément Gombeaud
CEA/Saclay-CNRS
Quark-Matter 09, April 09
Outline
• Introduction- Femtoscopy Puzzle at RHIC
• Motivation
• Transport numerical tool
– Boltzmann solution
– Dimensionless numbers
CG, J. Y. Ollitrault, Phys. Rev C 77, 054904
• HBT for central HIC
– Boltzmann versus hydro
– Partial resolution of the HBT-Puzzle
CG, Lappi, Ollitrault, arxiv:0901.4908v1
– Effect of the EOS
• Azimuthally sensitive HBT (AzHBT)
• Conclusion
Introduction
• HBT, the femtoscopic observables
P
y
z
HBT puzzle:
Experiment Ro/Rs=1
Ideal hydro Ro/Rs=1.5
x
Motivation
• Ideal hydrodynamics gives a good qualitative
description of soft observables in ultrarelativistic
heavy-ion collisions at RHIC
• But it is unable to quantitatively reproduce data: Full
thermalization not achieved
• Using a transport simulation, we study the
sensitivity of the HBT radii to the degree of
thermalization, and if this effect can explain,
even partially, the HBT puzzle
Monte-Carlo simulation method
• Numerical solution of the 2+1 dimensional Boltzmann
equation.
• The Boltzmann equation (v·∂)f=C[f] describes the
dynamics of a dilute gas statistically, through its 1particle phase-space distribution f(x,t,p)
• The Monte-Carlo method solves this equation by
– drawing randomly the initial positions and momenta of particles
according to the phase-space distribution
– following their trajectories through 2→2 elastic collisions
– averaging over several realizations.
Dimensionless quantities
characteristic size of the system R
We define 2 dimensionless
quantities
•Dilution D=d/
•Knudsen K=/R~1/Ncoll_part
Boltzmann requires D<<1
Ideal hydro requires K<<1
Average distance
between particles d
Mean free path 
Previous study of v2 for Au-Au
At RHIC gives
Central collisions  K=0.3
Drescher & al, Phys. Rev. C76, 024905 (2007)
Boltzmann versus hydro
Small sensitivity of the Pt dependence to the thermalization
The same behaviour is seen in both partially thermalized
Boltzmann and short lived ideal hydro simulation
Evolution vs K-1
Solid lines are fit with
F(K)=F0+F1/(1+F2*K)
K-1=3
b=0 Au-Au
At RHIC
Hydro limit
of the HBT radii
Regarding the values of F2
V2 goes to hydro three
times faster than HBT
v2hydro
Partial solution of the HBT
puzzle
Piotr Bozek & al arXiv:0902.4121v1
Similar results for K=0.3 (extracted from v2 study)
and for the short lived ideal hydro
Partial thermalization (=few collisions per particles)
explains most of the HBT Puzzle
ViscosityPartial
thermalization
Effect of the EOS
Realistic
EOS
Pratt arxiv:0811.3363
Our Boltzmann equation implies Ideal gas EOS (=3P)
Pratt find that EOS is more important than viscosity
Our K=0.3 (~viscous) simulation solves most of the Puzzle
AzHBT Observables
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Qu ic kTi me™ a nd a
TIFF (Unc om pres se d) de co mp re ss or
are n ee de d to s ee th is pi ctu re .
Quic kTi me™ and a
TIFF (Unc om pres sed) decompre ss or
are needed to s ee this pi cture .
QuickTime™ and a
TIFF (Uncompressed) decompressor
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TIFF (Uncompressed) decompressor
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Evolution vs K-1
Ro2/Rs2 evolve qualitatively as Ro/Rs
s misses the data even in the hydro limit
EOS effects
Conclusion
• The Pt dependence of the HBT radii is not a
signature of the hydro evolution
• Hydro prediction Ro/Rs=1.5 requires
unrealistically large number of collisions.
• Our K=0.3 (extracted from v2) explains most
of the HBT Puzzle.
• 3+1d simulation using boost invariance
Backup slides
Dimensionless numbers
• Parameters:
– Transverse size R
– Cross section σ (~length in 2d!)
– Number of particles N
The hydrodynamic
regime requires
both D«1 and Kn«1.
• Other physical quantities
– Particle density n=N/R2
– Mean free path λ=1/σn
– Distance between particles d=n-1/2
• Relevant dimensionless numbers:
– Dilution parameter D=d/λ=(σ/R)N-1/2
– Knudsen number Kn=λ/R=(R/σ)N-1
Since N=D-2Kn-2,
a huge number of
particles must be
simulated.
(even worse in 3d)
The Boltzmann equation requires D«1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport
results
Transport usually implies instantaneous collisions
Problem of causality
rKD2  D<<1 solves this problem
when K fixes the physics
Viscosity and partial
thermalization
• Non relativistic case

  therm

• Israel-Stewart corresponds to an
expansion in power of Knudsen number

Implementation
• Initial conditions: Monte-Carlo sampling
– Gaussian density profile (~ Glauber)
– 2 models for momentum distribution:
• Thermal Boltzmann (with T=n1/2)
• CGC
(A. Krasnitz & al, Phys. Rev. Lett. 87 19 (2001))
(T. Lappi Phys. Rev. C. 67 (2003) )
With a1=0.131, a2=0.087, b=0.465 and Qs=n1/2
• Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro/(1+1.4 Kn)
Smooth convergence to ideal hydro as Kn→0
The centrality dependence of v2 explained
1. Phobos data for v2
2. ε obtained using
Glauber or CGC
initial conditions
+fluctuations
3. Fit with
v2=v2hydro/(1+1.4 Kn)
assuming
1/Kn=(σ/S)(dN/dy)
with the fit parameters
σ and v2hydro/ε.
(Density in the azimuthal plane)
Kn~0.3 for central Au-Au collisions
v2 : 30% below ideal hydro!
AzHBT radii evolution vs K-1
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Better convergence to hydro in the direction of the flow
EOS effects
• Ideal gas
• RoRsRl product is conserved
S. V. Akkelin and Y. M. Sinyukov, Phys. Rev. C70, 064901 (2004)
In nature, there is a phase transition
• Realistic EOS
• s deacrese, but S constant at the transition (constant T)
– Increase of the volume V at constant T
Phase transition implies an increase of the radii values
AzHBT vs data
Pt in [0.15,0.25] GeV 20-30%
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Pt in [0.35,0.45] GeV 10-20%
HBT vs data