freeze-out in a hybrid model freeze-out workshop, 6.5.09 goethe-universität frankfurt hannah...

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


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)


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

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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


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)


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


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


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


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))


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


Temperatures

Chemical FO by Cleymans et al.

Rapidity distribution of the transition temperatures

Isochronuous Freeze-out

Gradual Freeze-out


Chemical Potentials

Rapidity distribution of the chemical potentials at the transition


Gradual Freeze-out


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



Full symbols: 40 AGeV

Open symbols: 11 AGeV


Final State Interactions


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


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


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)


<mT> Excitation Function

(H.P

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al.,

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Data

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Hadronic hydro calculation with different freeze-out scenarios

Freeze-out treatment is important

Dynamics (viscosity) and equation of state are crucial input


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


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


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

Backup


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

freeze-out in a hybrid model freeze-out workshop, 6.5.09 goethe-universität frankfurt hannah...

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