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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 HBT for central HIC

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Partial thermalization, a key ingredient of the HBT Puzzle

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  1. Partial thermalization,a key ingredient of the HBT Puzzle Clément Gombeaud CEA/Saclay-CNRS Quark-Matter 09, April 09

  2. Outline • Introduction- Femtoscopy Puzzle at RHIC • Motivation • Transport numerical tool • Boltzmann solution • Dimensionless numbers • HBT for central HIC • Boltzmann versus hydro • Partial resolution of the HBT-Puzzle • Effect of the EOS • Azimuthally sensitive HBT (AzHBT) • Conclusion CG, J. Y. Ollitrault, Phys. Rev C 77, 054904 CG, Lappi, Ollitrault, arxiv:0901.4908v1

  3. Introduction P y • HBT, the femtoscopic observables x z HBT puzzle: Experiment Ro/Rs=1 Ideal hydro Ro/Rs=1.5

  4. 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

  5. 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 1-particle 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.

  6. 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 Previous study of v2 for Au-Au At RHIC gives Mean free path  Average distance between particles d Central collisions  K=0.3 Drescher & al, Phys. Rev. C76, 024905 (2007)

  7. 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

  8. Evolution vs K-1 Hydro limit of the HBT radii K-1=3 b=0 Au-Au At RHIC Solid lines are fit with F(K)=F0+F1/(1+F2*K) Regarding the values of F2 V2 goes to hydro three times faster than HBT v2hydro

  9. Piotr Bozek & al arXiv:0902.4121v1 Partial solution of the HBT puzzle 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

  10. Pratt arxiv:0811.3363 ViscosityPartial thermalization Effect of the EOS Realistic EOS 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

  11. AzHBT Observables P y x z

  12. Evolution vs K-1 Ro2/Rs2 evolve qualitatively as Ro/Rs smisses the data even in the hydro limit EOS effects

  13. 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

  14. Backup slides

  15. Dimensionless numbers The hydrodynamic regime requires both D«1 and Kn«1. Since N=D-2Kn-2, a huge number of particles must be simulated. (even worse in 3d) • Parameters: • Transverse size R • Cross section σ (~length in 2d!) • Number of particles N • 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 The Boltzmann equation requires D«1 This is achieved by increasing N (parton subdivision)

  16. 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

  17. Viscosity and partial thermalization • Non relativistic case • Israel-Stewart corresponds to an expansion in power of Knudsen number

  18. 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.8719 (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

  19. Elliptic flow versus Kn v2=v2hydro/(1+1.4 Kn) Smooth convergence to ideal hydro as Kn→0

  20. The centrality dependence of v2 explained • Phobos data for v2 • εobtained using Glauber or CGC initial conditions +fluctuations • 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!

  21. AzHBT radii evolution vs K-1 Better convergence to hydro in the direction of the flow

  22. EOS effects • Ideal gas • RoRsRl product is conserved 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 S. V. Akkelin and Y. M. Sinyukov, Phys. Rev. C70, 064901 (2004)

  23. AzHBT vs data Pt in [0.15,0.25] GeV 20-30% Pt in [0.35,0.45] GeV 10-20%

  24. HBT vs data

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