Freeze-Out in a Hybrid Model

1
Freeze-Out in a Hybrid Model

• Freeze-out Workshop, 6.5.09
• Goethe-Universität Frankfurt
• Hannah Petersen

2
Outline

• Short overview of the hybrid model
• Two freeze-out prescriptions
• Details about the implementation
• T and mB distributions
• Influence of transition criterion
• Multiplicities
• Rapidity and transverse mass spectra
• HBT and elliptic flow
• Conclusion and outlook

3
Hybrid Approach

• Essential to draw conclusions from final state
  particle distributions about initially created
  medium
• The idea here Fix the initial state and
  freeze-out
• ? learn something about the EoS and the effect
  of viscous dynamics

2) Hydrodynamic evolution or
Transport calculation
3) Freeze-out via hadronic cascade
(UrQMD)
1) Non-equilibrium initial conditions
via UrQMD
(H.P. et al., PRC 78044901, 2008, arXiv
0806.1695)
4
Equations of State

• Ideal relativistic one fluid dynamics
• and
• HG Hadron gas including the same degrees of
  freedom as in UrQMD (all hadrons with masses up
  to 2.2 GeV)
• CH Chiral EoS from SU(3) hadronic Lagrangian
  with first order transition and critical endpoint
• BM Bag Model EoS with a strong first order phase
  transition between QGP and hadronic phase

D. Rischke et al., NPA 595, 346, 1995, D.
Zschiesche et al., PLB 547, 7, 2002 Papazoglou et
al., PRC 59, 411, 1999

• Hadronization happens (if phase transition is
  included) during the hydrodynamic evolution
• Transition to transport happens in the hadronic
  stage, same degrees of freedeom on both sides
  of the hypersurface

5
Freeze-out

• Transition from hydro to transport when e lt 730
  MeV/fm³ ( 5 e0) in all cells of one transverse
  slice (Gradual freeze-out, GF)
• ? iso-eigentime criterion
• Transition when e lt 5 e0 in all
  cells(Isochronuous freeze-out, IF)

• Particle distributions are generated according
  to the Cooper-Frye formula
• with boosted Fermi or Bose distributions f(x,p)
  including mB and mS
• Rescatterings and final decays calculated via
  hadronic cascade (UrQMD)

6
Our Approach

• Need a Monte Carlo procedure that runs in
  reasonable computing time because we are
  interested in event-by-event physics
• Isochronous or gradual freeze-out with hadronic
  cascade calculation for rescatterings and
  resonance decays
• Loop over the grid and for each cell the
  following steps are done

7
Steps for the Particle Production

1. Numbers of each particle species in the cell
2. Sum to get the total particle number
3. Particle production according to Poisson
   distribution
4. Particle type chosen according to probabilities
5. Isospin randomly assigned, charge conservation
6. Generate four-momenta
7. Particle vector information is transferred back
   to UrQMD

8
Conservation Laws

• Three loops to assure net-strangeness and baryon
  number at the same time
• Energy conservation on the average (for gradual
  freeze-out in principle not on the hypersurface,
  but baryon number conservation helps)
• First strange particles
• Antistrange particles
• Fill up baryon number
• Charge conservation with tuned isospin

9
Isochronuous Freeze-out
Distribution of the cells at freeze-out at Elab
40 AGeV
? Important inhomogeneities are naturally taken
into account (A.Dumitru et al., Phys. Rev. C
73, 024902 (2006))
10
Freeze-out Line

• Parametrization of chemical freeze-out line
  taken from
• Cleymans et al,
• J.Phys. G 32, S165, 2006
• Green points are from
• A.Dumitru et al., PRC 73, 024902, 2006
• ? Mean values and widths are in line with other
  calculations

5e0
Black Gradual FO Red Isochronuous FO
11
Temperatures
Rapidity distribution of the transition
temperatures
Chemical FO by Cleymans et al.
Isochronuous Freeze-out
Gradual Freeze-out
12
Chemical Potentials
Rapidity distribution of the chemical potentials
at the transition
Isochronuous Freeze-out
Gradual Freeze-out
13
Transition Times

• Transition times along beam direction for the
  gradual freeze-out
• At lower energies outer layers freeze-out first
• At higher energies transition begins in the
  center
• ?Mimics iso-eigentime criterion

14
Isochronuous Freeze-out
Full symbols 40 AGeV Open symbols 11 AGeV
15
Final State Interactions
16
Multiplicities vs. Energy
full lines hybrid model (IF) squares hybrid
model (GF) dotted lines UrQMD-2.3 symbols
experimental data

• Both models are purely hadronic without phase
  transition, but different underlying dynamics
• Gradual transition improves multistrange hyperon
  yields
• ? Results for particle multiplicities from AGS to
  SPS are similar
• ? Strangeness is enhanced in the hybrid approach
  due to local equilibration

W
X
L
(H.P. et al., PRC 78044901, 2008)
p
K
P
Central (blt3.4 fm) PbPb/AuAu collisions
Data from E895, NA49
17
Rapidity Spectra
full lines hybrid model (IF) squares hybrid
model (GF) dotted lines UrQMD-2.3 symbols
experimental data
? Rapidity spectra for pions and kaons have a
very similar shape in both calculations
18
mT Spectra
Blue pions Green protons Red kaons
11 AGeV
160 AGeV
Full line hybrid model (IF) Dashed line hybrid
model (GF) Dotted line UrQMD-2.3
40 AGeV
(H.P. et al., PRC 78044901, 2008)

• mT spectra are very similar at lower energies
  (11,40 AGeV)
• ltmTgt is higher in hydro calculation at
  Elab160 AGeV

Central (blt3.4 fm) PbPb/AuAu collisions
19
ltmTgt Excitation Function
(H.P. et al., arXiv 0902.4866, JPG in print)
Hadronic hydro calculation with different
freeze-out scenarios ? Freeze-out treatment is
important
Dynamics (viscosity) and equation of state are
crucial input
Data from E866, NA49
20
RO/RS Ratio

• Hydro phase leads to smaller ratios
• Hydro to transport transition does not matter, if
  final rescattering is taken into account
• EoS dependence is visible, but not as strong as
  previuosly predicted (factor of 5)

Data from NA49
(Q. Li, H.P. et al., PLB 674, 111, 2009)
21
Elliptic Flow

• Smaller mean free path in the hot and dense phase
  leads to higher elliptic flow
• At lower energies hybrid approach reproduces the
  pure UrQMD result
• Gradual freeze-out leads to a better description
  of the data

(H.P. et.al., arXiv0901.3821, PRC in print)
Data from E895, E877, NA49, Ceres, Phenix,
Phobos, Star
22
Conclusions and Outlook

• Hadronization is done during the hydrodynamic
  evolution according to equation of state
• Two prescriptions of the transition from hydro to
  transport have been developed
• Gradual freeze-out leads overall to a better
  description of experimental data
• Improve hypersurface (Schlei-Code) and test
  sensitivity on criteria
• Couple freeze-out routine to parton cascade
• Dynamical coupling of transport and hydro
  approach

23
Backup
24
Initial State

• Contracted nuclei have passed through each other
• Energy is deposited
• Baryon currents have separated
• Energy-, momentum- and baryon number densities
  are mapped onto the hydro grid
• Event-by-event fluctuations are taken into
  account
• Spectators are propagated separately in the
  cascade

(nucl-th/0607018, nucl-th/0511021)
Elab40 AGeV b0 fm
(J.Steinheimer, H.P. et al., PRC 77,034901,2008)
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