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Partial thermalizationa key ingredient
of the HBT Puzzle
Cleacutement Gombeaud
CEASaclay-CNRS
Quark-Matter 09 April 09
Outlinebull Introduction- Femtoscopy Puzzle at RHICbull Motivationbull Transport numerical tool
ndash Boltzmann solutionndash Dimensionless numbers
bull HBT for central HICndash Boltzmann versus hydrondash Partial resolution of the HBT-Puzzle
ndash Effect of the EOS
bull Azimuthally sensitive HBT (AzHBT)bull Conclusion
CG J Y Ollitrault Phys Rev C 77 054904
CG Lappi Ollitrault arxiv09014908v1
P
y
xz
Introductionbull HBT the femtoscopic observables
HBT puzzle
Experiment RoRs=1Ideal hydro RoRs=15
Motivationbull Ideal hydrodynamics gives a good qualitative
description of soft observables in ultrarelativistic heavy-ion collisions at RHIC
bull But it is unable to quantitatively reproduce data Full thermalization not achieved
bull 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
bull Numerical solution of the 2+1 dimensional Boltzmann equation
bull The Boltzmann equation (vpart)f=C[f] describes the dynamics of a dilute gas statistically through its 1-particle phase-space distribution f(xtp)
bull The Monte-Carlo method solves this equation byndash drawing randomly the initial positions and momenta of particles
according to the phase-space distributionndash following their trajectories through 2rarr2 elastic collisionsndash averaging over several realizations
Monte-Carlo simulation method
Dimensionless quantities
Average distancebetween particles d
Mean free path
We define 2 dimensionlessquantities
bullDilution D=dbullKnudsen K=R~1Ncoll_part
characteristic size of the system R
Boltzmann requires Dltlt1Ideal hydro requires Kltlt1
Previous study of v2 for Au-AuAt RHIC gives
Central collisions K=03
Drescher amp al Phys Rev C76 024905 (2007)
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Outlinebull Introduction- Femtoscopy Puzzle at RHICbull Motivationbull Transport numerical tool
ndash Boltzmann solutionndash Dimensionless numbers
bull HBT for central HICndash Boltzmann versus hydrondash Partial resolution of the HBT-Puzzle
ndash Effect of the EOS
bull Azimuthally sensitive HBT (AzHBT)bull Conclusion
CG J Y Ollitrault Phys Rev C 77 054904
CG Lappi Ollitrault arxiv09014908v1
P
y
xz
Introductionbull HBT the femtoscopic observables
HBT puzzle
Experiment RoRs=1Ideal hydro RoRs=15
Motivationbull Ideal hydrodynamics gives a good qualitative
description of soft observables in ultrarelativistic heavy-ion collisions at RHIC
bull But it is unable to quantitatively reproduce data Full thermalization not achieved
bull 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
bull Numerical solution of the 2+1 dimensional Boltzmann equation
bull The Boltzmann equation (vpart)f=C[f] describes the dynamics of a dilute gas statistically through its 1-particle phase-space distribution f(xtp)
bull The Monte-Carlo method solves this equation byndash drawing randomly the initial positions and momenta of particles
according to the phase-space distributionndash following their trajectories through 2rarr2 elastic collisionsndash averaging over several realizations
Monte-Carlo simulation method
Dimensionless quantities
Average distancebetween particles d
Mean free path
We define 2 dimensionlessquantities
bullDilution D=dbullKnudsen K=R~1Ncoll_part
characteristic size of the system R
Boltzmann requires Dltlt1Ideal hydro requires Kltlt1
Previous study of v2 for Au-AuAt RHIC gives
Central collisions K=03
Drescher amp al Phys Rev C76 024905 (2007)
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
P
y
xz
Introductionbull HBT the femtoscopic observables
HBT puzzle
Experiment RoRs=1Ideal hydro RoRs=15
Motivationbull Ideal hydrodynamics gives a good qualitative
description of soft observables in ultrarelativistic heavy-ion collisions at RHIC
bull But it is unable to quantitatively reproduce data Full thermalization not achieved
bull 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
bull Numerical solution of the 2+1 dimensional Boltzmann equation
bull The Boltzmann equation (vpart)f=C[f] describes the dynamics of a dilute gas statistically through its 1-particle phase-space distribution f(xtp)
bull The Monte-Carlo method solves this equation byndash drawing randomly the initial positions and momenta of particles
according to the phase-space distributionndash following their trajectories through 2rarr2 elastic collisionsndash averaging over several realizations
Monte-Carlo simulation method
Dimensionless quantities
Average distancebetween particles d
Mean free path
We define 2 dimensionlessquantities
bullDilution D=dbullKnudsen K=R~1Ncoll_part
characteristic size of the system R
Boltzmann requires Dltlt1Ideal hydro requires Kltlt1
Previous study of v2 for Au-AuAt RHIC gives
Central collisions K=03
Drescher amp al Phys Rev C76 024905 (2007)
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Motivationbull Ideal hydrodynamics gives a good qualitative
description of soft observables in ultrarelativistic heavy-ion collisions at RHIC
bull But it is unable to quantitatively reproduce data Full thermalization not achieved
bull 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
bull Numerical solution of the 2+1 dimensional Boltzmann equation
bull The Boltzmann equation (vpart)f=C[f] describes the dynamics of a dilute gas statistically through its 1-particle phase-space distribution f(xtp)
bull The Monte-Carlo method solves this equation byndash drawing randomly the initial positions and momenta of particles
according to the phase-space distributionndash following their trajectories through 2rarr2 elastic collisionsndash averaging over several realizations
Monte-Carlo simulation method
Dimensionless quantities
Average distancebetween particles d
Mean free path
We define 2 dimensionlessquantities
bullDilution D=dbullKnudsen K=R~1Ncoll_part
characteristic size of the system R
Boltzmann requires Dltlt1Ideal hydro requires Kltlt1
Previous study of v2 for Au-AuAt RHIC gives
Central collisions K=03
Drescher amp al Phys Rev C76 024905 (2007)
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
bull Numerical solution of the 2+1 dimensional Boltzmann equation
bull The Boltzmann equation (vpart)f=C[f] describes the dynamics of a dilute gas statistically through its 1-particle phase-space distribution f(xtp)
bull The Monte-Carlo method solves this equation byndash drawing randomly the initial positions and momenta of particles
according to the phase-space distributionndash following their trajectories through 2rarr2 elastic collisionsndash averaging over several realizations
Monte-Carlo simulation method
Dimensionless quantities
Average distancebetween particles d
Mean free path
We define 2 dimensionlessquantities
bullDilution D=dbullKnudsen K=R~1Ncoll_part
characteristic size of the system R
Boltzmann requires Dltlt1Ideal hydro requires Kltlt1
Previous study of v2 for Au-AuAt RHIC gives
Central collisions K=03
Drescher amp al Phys Rev C76 024905 (2007)
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Dimensionless quantities
Average distancebetween particles d
Mean free path
We define 2 dimensionlessquantities
bullDilution D=dbullKnudsen K=R~1Ncoll_part
characteristic size of the system R
Boltzmann requires Dltlt1Ideal hydro requires Kltlt1
Previous study of v2 for Au-AuAt RHIC gives
Central collisions K=03
Drescher amp al Phys Rev C76 024905 (2007)
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Boltzmann versus hydro
The same behaviour is seen in both partially thermalized Boltzmann and short lived ideal hydro simulation
Small sensitivity of the Pt dependence to the thermalization
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Evolution vs K-1
Solid lines are fit withF(K)=F0+F1(1+F2K)
V2 goes to hydro threetimes faster than HBT
K-1=3b=0 Au-AuAt RHIC
v2hydro
Hydro limitof the HBT radii
Regarding the values of F2
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Partial solution of the HBT puzzle
Piotr Bozek amp al arXiv09024121v1
Similar results for K=03 (extracted from v2 study) and for the short lived ideal hydro
Partial thermalization (=few collisions per particles) explains most of the HBT Puzzle
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Effect of the EOSRealistic
EOS
ViscosityPartial thermalization
Our Boltzmann equation implies Ideal gas EOS (=3P)Pratt find that EOS is more important than viscosity
Our K=03 (~viscous) simulation solves most of the Puzzle
Pratt arxiv08113363
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
AzHBT Observables
y
x
P
z
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
QuickTimetrade and aTIFF (Uncompressed) decompressorare needed to see this picture
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Evolution vs K-1
Ro2Rs
2 evolve qualitatively as RoRs
s misses the data even in the hydro limit
EOS effects
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Conclusion
bull The Pt dependence of the HBT radii is not a signature of the hydro evolution
bull Hydro prediction RoRs=15 requires unrealistically large number of collisions
bull Our K=03 (extracted from v2) explains most of the HBT Puzzle
bull 3+1d simulation using boost invariance
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Backup slides
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Dimensionless numbersbull Parameters
ndash Transverse size Rndash Cross section σ (~length in 2d)ndash Number of particles N
bull Other physical quantitiesndash Particle density n=NR2
ndash Mean free path λ=1σnndash Distance between particles d=n-12
bull Relevant dimensionless numbersndash Dilution parameter D=dλ=(σR)N-12
ndash Knudsen number Kn=λR=(Rσ)N-1
The hydrodynamic regime requires both Dlaquo1 and Knlaquo1
Since N=D-2Kn-2 a huge number of particles must be simulated
(even worse in 3d)The Boltzmann equation requires Dlaquo1
This is achieved by increasing N (parton subdivision)
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Impact of dilution on transport results
Transport usually implies instantaneous collisions
Problem of causality
rKD2 Dltlt1 solves this problem when K fixes the physics
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Viscosity and partial thermalization
bull Non relativistic case
bull Israel-Stewart corresponds to an expansion in power of Knudsen number
euro
ηρasympυ therm
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Implementationbull Initial conditions Monte-Carlo sampling
ndash Gaussian density profile (~ Glauber)ndash 2 models for momentum distribution
bull Thermal Boltzmann (with T=n12)
bull CGC (A Krasnitz amp al Phys Rev Lett 87 19 (2001))
(T Lappi Phys Rev C 67 (2003) )
With a1=0131 a2=0087 b=0465 and Qs=n12
bull Ideal gas EOS
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
Elliptic flow versus Kn
v2=v2hydro(1+14 Kn)
Smooth convergence to ideal hydro as Knrarr0
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
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+14 Kn)
assuming
1Kn=(σS)(dNdy)
with the fit parameters σ and v2
hydroε
Kn~03 for central Au-Au collisions
v2 30 below ideal hydro
(Density in the azimuthal plane)
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
AzHBT radii evolution vs K-1
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Better convergence to hydro in the direction of the flow
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
EOS effects
bull Ideal gasbull RoRsRl product is conserved
In nature there is a phase transition
bull Realistic EOSbull s deacrese but S constant at the transition (constant T)
ndash Increase of the volume V at constant T
Phase transition implies an increase of the radii values
S V Akkelin and Y M Sinyukov Phys Rev C70 064901 (2004)
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
AzHBT vs data
QuickTimetrade and aTIFF (Uncompressed) decompressor
are needed to see this picture
Pt in [015025] GeV 20-30
Pt in [035045] GeV 10-20
HBT vs data
HBT vs data
