HBT results from UrQMD

HBT results from UrQMD

by Qingfeng Li(@ FIAS/Frankfurt & Huzhou)

In cooperation with M. Bleicher and H. Stoecker

QF for WPCF2008, Krakow04/19/23

outline

Brief introduction to the UrQMD and potential updates.

HBT results from UrQMD with cascade and with potentials.

The effects of the non-Gaussian and the resonance decay on HBT radii.

Other results from UrQMD with and without potentials: stopping, elliptic flow.


The UrQMD modelUrQMD : Ultra-relativistic Quantum Molecular Dynamics

•It is a non-equilibrium transport model

•It includes 55 baryon species (with mass up to 2.25GeV) and 32 meson species (with mass up to 1.91GeV)

•Particles interact via:

- Mean Field modification - Collisions (with measured and calculated cross sections)

•Particles produce via:

- Formation and decay of resonance

- Excitation and fragmentation of string

• It provides full phase-space dynamics of heavy-ion collisions

• it can be used to study HICs at energies from SIS to RHIC

•The newest version 2.3 has been released. (http://th.physik.uni-frankfurt.de/~urqmd/)


EoS It is well-known that, in low-energy nuclear physics,

the mean-field effect is essential. Phenomenologically, the mean field includes: - bulk term (density dependent) - surface term

- Yukawa term - Pauli term - symmetry energy term - momentum dependent term

And, the Coulomb potential for charged particles


One example: to solve the Flow “puzzle” at low energies

At Eb<10 A GeV, the flow can be wellreproduced with a specified potential.

22

22

2

yx

yx

pp

ppv


Treatment of the “pre-formed” hadrons

before string fragmentation At high SPS and RHIC energies, particle production is do

minated by the string mechanism. The formation time of the hadron is determined by the “y

o-yo” mode. During this time, the particles are taken as “pre-formed”. The transport of the “pre-formed” particles is treated to be “free-streaming”.

The reduced cross sections are only included for leading hadrons.


Why to consider the potential for “pre-formed” hadrons?

sQGP tells us that there is a strong coupling between particles at early stage.

Small elliptic flow at RHIC was predicted by UrQMD.

The gggg interaction is believed not enough by Xu and Greiner (PRC71, 064901 (2005) ).

There is no free quarks/gluons in UrQMD. Shorter formation time leads to increase the flow

but also multiplicities drastically.


How to consider the “pre-formed” hadronic potential?

To modify the interactions at early stage, more collisions (by considering a shorter formation time or larger cross sections for “pre-formed” particles) or a mean-field potential for “pre-formed” hadrons might be taken into account. The former idea has been checked in the AMPT and the HRM models. Here we would like to consider the latter idea.

As the first step, ① the density dependent term used for formed baryons is used for “pr

e-formed” particles. ② The “pre-formed” mesons act like “pre-formed” baryons but with a r

eduction factor (2/3) due to the quark-number difference.③ The potential interaction between formed and “pre-formed” particle

s is neglected.④ The “pre-formed” particles also contribute to the hadronic density (f

or “pre-formed” mesons, the 2/3 factor is considered).


Meanwhile, to check Hybrid model: Hydro+UrQMD

Ideal (3+1) D hydrodynamic evolution. Time scales in hydro process: from ~6 to 12 fm/c at SPS e

nergies. Hadron gas equation of state (EoS) (No phase transition)) Hydrodynamic evolution until < 730 MeV/fm³ (≈ 5 * 0) in

all cells After the hydro freeze-out, hadronic cascade follows. Typical times before cascade freezeout: 20-25 fm/c Pion production changes slightly: total yields: less; mome

ntum distribution: flatter at high SPS energies.Thanks: Hannah Pertersen Jan Steinhimer

Also ask them for details,


Waiting for the EoS which originates from the first principle lQCD

Although: The form of the potentials for the new phase is s

imple and rough (in my version) The EoS with the phase transition is needed (in

Jan&Hannah’s version) However: it is quite necessary to study the effect of the me

an field on the two-particle correlation right now!


The analyzing program and the Gaussian parameterization

CRAB analyzing program: http://www.nscl.msu.edu/~pratt/freecodes/crab/home.html

Three-dimensional Gaussian parameterization

LCMS is employed in normal calculations

Coulomb effect in FSI is considered for charged two-kaon correlation with a Bowler-Sinyukov method

non-Gaussian effect is discussed under the Edgeworth expansion

)2exp(1),,( 2222222LOOLLLSSOOLSO qqRqRqRqRqqqC

))2exp(1)((

)1(),,(2222222

LOOLLLSSOOinvcoul

LSO

qqRqRqRqRqK

qqqC

The fitting work can be done by the ROOT or the ORIGIN software (using -squared method)


Non-Gaussian Effect

0 20 40 60 80 100 120q

inv (MeV/c)

fittings: Rinv

(fm)

No expansion 6.58

to 4th order 6.81

to 6th order 7.09

to 8th order 7.41

SM-EoS, (M)

0 20 40 60 80 100

1.0

1.2

1.4

1.6

1.8

2.0

C

fittings: Rinv

(fm)

No expansion 7.36

to 4th order 7.66

to 6th order 8.05

to 8th order 8.54

Cas, (M)E

b=2A GeV

1.0

1.2

1.4

1.6

1.8

2.0

1.0

1.2

1.4

1.6

1.8

2.0

0 30 60 90

1.0

1.2

1.4

1.6

1.8

2.0

outward: q

O; q

S,q

L<5 MeV/c

Eb=2 A GeV

q (MeV/c)

longitudial: q

L; q

O,q

S<5 MeV/c

Cas, (M) SM-EoS, (M)

C

sideward: q

S; q

O,q

L<5 MeV/c

0 30 60 90 120

Non-Gaussian effect is visible in the 3D-correlation functionsIt’s strongest in longitudinal direction and weakest in sideward direction.


Effect of resonance decay on HBT radii

0

2

4

6

8

10

RL (fm

)

1/2 0

0

2 0

Eb=2A GeV, UrQMD (Cascade)

RS (fm

)

exp.

kT (MeV/c)

0

2

4

6

8

10

0 200 4000

2

4

6

8

RO/R

SR

O (fm

)

0 200 4000.8

1.0

1.2

1.4

0

2

4

6

8

10

(8A GeV)(6A GeV)(4A GeV)(2A GeV) exp. Cas,

0 Cas,(M) SM-EoS,(M)

RO/R

SR

L (fm

)R

O (fm

)R

S (fm

)

kT (MeV/c)

0

2

4

6

8

0

2

4

6

8

0 200 4000.8

1.0

1.2

1.4

0 200 4000 200 4000 200 400

1.1 1.2 1.3 1.4 1.5 1.60

1

2

3

4

5

(fm

/c)

M (GeV)

(M)

0(=115 MeV)

0

2 0

=1/for

Treatments of resonance decay affect HBT radii at small kT, but not the RO/RS ratio


HBT results from UrQMD

0

2

4

6

8

10s200E158E80E40E30E20E8E6E4E2 s130

f-B SM-EoS & M Coul. pf-part & f-B SM-EoS & no M Coul.

: exp. : Cascade f-B SM

0

2

4

6

8

0 2500

2

4

6

8

0 250 0 250 0 250 0 250 0 250 0 250 0 250 0 250 0 500 0 500

RO (fm

)R

S (fm

)R

L (fm

)

kT (MeV/c)

AGS SPS RHIC

kT-dep. radii: steeperRO at large kT:

RS at small kT:

In the pion case:


Improvement to the mT-scaling

Without “pre-formed” hadron potential: RL: of kaons and Lambdas: Large RO: of all particles : Large RS: of Lambdas : Large

With “pre-formed” Hadron potential: RL: of Kaons and Lambda: follow RO: of all particles : follow RS: of pions and Kaons : followthe mT-scaling

Left Plots:

Right Plots:

T.Csorgo etc, PRC 54, 1390(1996)Without the consideration of the FSI in hydro-dynamics

22TT kmm


To solve the HBT t-puzzleIn the pion case:


Not only for the source…

The marked areaillustrates the uncertaintiesfrom non-Gaussian effectand corrections on FSI

The inclusion of “pre-formed” particle interactions cures the deviations and allows for a consistent understanding of the data.


Why so ?Under the assumptions of thermalization and Gaussian-source shape, the HBT radii can be expressed analytically as

RO term can be expanded as ：

Due to the strong phase-correlation induced by the potentials, the term -2<Txt> might be comparable to the term <t

2t2>.

An important consensus:Due to the strong x-t correlation, RO/RS1 does not mean t0


Hydro EoS (Hadron-Gas) contributionHydro-process helps todrive down the Ro/Rs ratio;

The ratio from hybrid model is still larger than data since it is cascade after hydro freeze-out.

In the hybrid model:More EoS should be checked;More events and particle pairsShould be analyzed.

Events:4000-6000Pairs: 100M (for all kT bins)


stopping at SPS energies

0

1

2

3(158A GeV)(80A GeV)(40A GeV)(30A GeV)

dn/d

y of p

dn/d

y of anti-

p

y

(20A GeV)

Cascade SM-EoS

T<7%

-2 -1 0 10

10

20

30

40

50

60

-2 -1 0 1 -2 -1 0 1 -2 -1 0 1 -2 -1 0 1 2

Results are still preliminary

In cascade mode:Gaussian-like atall energiesIn potential mode:Two-bump occurs for pat high SPS energies


Elliptic flow at RHIC

Of course, the collision of partons is necessary

The v2 at pt~1GeV/c is driven up with the pre-formed hadronic potentialThe potential effect is strong in central HICs


Conclusions

To understand the “HBT t-puzzle” and the mT -scaling, one needs to consider more about the interactions of particles at the early stage of HICs

The resonance decay contributes to the non-Gaussian phenomenon and the HBT radii but not the “HBT t-puzzle”.

A consistently thermal dynamic description of high energetic HICs is still awaiting.


ThanksReference list:

e-Print: arXiv:0808.3457 [nucl-th]

Phys. Lett. B 663, 395 (2008)

Phys. Lett. B 659, 525 (2008)

J. Phys. G 34, 537 (2007)

J. Phys. G 34, 2037 (2007)

Phys. Rev. C 74, 064908 (2006)

Phys. Rev. C 73, 064908 (2006)

HBT results from UrQMD

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