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Freeze-Out in a Hybrid Model
Freeze-out Workshop, 6.5.09Goethe-Universität Frankfurt
Hannah Petersen
Hannah Petersen Freeze-out Workshop, 06.05.09
Outline
• Short overview of the hybrid model• Two freeze-out prescriptions• Details about the implementation• T and B distributions• Influence of transition criterion• Multiplicities• Rapidity and transverse mass spectra• HBT and elliptic flow• Conclusion and outlook
Hannah Petersen Freeze-out Workshop, 06.05.09
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
1) Non-equilibrium
initial conditions
via UrQMD
2) Hydrodynamic evolution or Transport calculation
3) Freeze-out via
hadronic cascade
(UrQMD) (H.P. et al., PRC 78:044901, 2008, arXiv: 0806.1695)
Hannah Petersen Freeze-out Workshop, 06.05.09
Equations of StateIdeal 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. R
isch
ke e
t al., N
PA
59
5, 3
46
, 1
99
5,
D. Z
schie
sche e
t al., PLB
54
7, 7
, 2
00
2
Papazo
glo
u e
t al., PR
C 5
9, 4
11
, 1
99
9
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
Hannah Petersen Freeze-out Workshop, 06.05.09
Freeze-out
1) Transition from hydro to transport when < 730 MeV/fm³ (≈ 5 * 0) in all cells of one transverse slice (Gradual freeze-out, GF) iso-eigentime criterion
2) Transition when < 5* 0 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 B and S
• Rescatterings and final decays calculated via hadronic cascade (UrQMD)
Hannah Petersen Freeze-out Workshop, 06.05.09
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
Hannah Petersen Freeze-out Workshop, 06.05.09
Steps for the Particle Production
1) Numbers of each particle species in the cell2) Sum to get the total particle number3) Particle production according to Poisson
distribution4) Particle type chosen according to
probabilities5) Isospin randomly assigned, charge
conservation6) Generate four-momenta7) Particle vector information is transferred
back to UrQMD
Hannah Petersen Freeze-out Workshop, 06.05.09
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
Hannah Petersen Freeze-out Workshop, 06.05.09
Isochronuous Freeze-outDistribution 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))
Hannah Petersen Freeze-out Workshop, 06.05.09
Freeze-out Line
• Parametrization of chemical freeze-out line taken fromCleymans 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
5*0
Black: Gradual FO
Red: Isochronuous FO
Hannah Petersen Freeze-out Workshop, 06.05.09
Temperatures
Chemical FO by Cleymans et al.
Rapidity distribution of the transition temperatures
Isochronuous Freeze-out
Gradual Freeze-out
Hannah Petersen Freeze-out Workshop, 06.05.09
Chemical Potentials
Rapidity distribution of the chemical potentials at the transition
Isochronuous Freeze-out
Gradual Freeze-out
Hannah Petersen Freeze-out Workshop, 06.05.09
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
Hannah Petersen Freeze-out Workshop, 06.05.09
Isochronuous Freeze-out
Full symbols: 40 AGeV
Open symbols: 11 AGeV
Hannah Petersen Freeze-out Workshop, 06.05.09
Multiplicities vs. Energy full lines: hybrid model (IF)
squares: hybrid model (GF)
dotted lines: UrQMD-2.3symbols: experimental
data
K PCentral (b<3.4 fm) Pb+Pb/Au+Au collisions (H
.P.
et
al.,
PR
C 7
8:0
44901,
2008)
• 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
Data from E895, NA49
Hannah Petersen Freeze-out Workshop, 06.05.09
Rapidity Spectra
Rapidity spectra for pions and kaons have a very similar shape in both calculations
full lines: hybrid model (IF)
squares: hybrid model (GF)
dotted lines: UrQMD-2.3symbols: experimental
data
Hannah Petersen Freeze-out Workshop, 06.05.09
mT Spectra Blue: pionsGreen: protonsRed: kaons
• mT spectra are very similar at lower energies (11,40 AGeV)
• <mT> is higher in hydro calculation at Elab=160 AGeV
11 AGeV
40 AGeV
160 AGeV
Central (b<3.4 fm) Pb+Pb/Au+Au collisions
Full line: hybrid model (IF)Dashed line: hybrid model (GF)Dotted line: UrQMD-2.3
(H.P
. et
al.,
PR
C 7
8:0
44901,
2008)
Hannah Petersen Freeze-out Workshop, 06.05.09
<mT> Excitation Function
(H.P
. et
al.,
arX
iv:
09
02
.48
66
, JP
G in
p
rin
t)
Data
fro
m E
86
6,
NA
49
Hadronic hydro calculation with different freeze-out scenarios
Freeze-out treatment is important
Dynamics (viscosity) and equation of state are crucial input
Hannah Petersen Freeze-out Workshop, 06.05.09
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)(Q. Li, H.P. et al., PLB 674, 111, 2009)
Data from NA49
Hannah Petersen Freeze-out Workshop, 06.05.09
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., arXiv:0901.3821, PRC in print)
Data from E895, E877, NA49, Ceres, Phenix, Phobos, Star
Hannah Petersen Freeze-out Workshop, 06.05.09
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
Hannah Petersen Freeze-out Workshop, 06.05.09
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
(J.Steinheimer, H.P. et al., PRC 77,034901,2008)
(nucl-th
/0607018
, nucl-th
/05110
21)
Elab=40 AGeV b=0 fm