HBT results from UrQMD

Marcus Bleicher, WPCF 08/2007

HBT results from UrQMDHBT results from UrQMD

Marcus Bleicher & Qingfeng Li (FIAS)

Institut für Theoretische Physik

Goethe Universität Frankfurt

Germany


Thanks to the UrQMD groupThanks to the UrQMD group

• Katharina Schmidt

• Manuel Reiter

• Sascha Vogel

• Xianglei Zhu

• Daniel Krieg

• Horst Stoecker

• Hannah Petersen

• Diana Schumacher

• Stephane Haussler

• Mohamed Abdel-Aziz

• Qingfeng Li


OutlineOutline

• HBT: How, Why, What?

• UrQMD model calculations

• HBT puzzle(s)

• Model explanations on the HBT puzzle

• Summary and outlook


The toolThe tool

UrQMD : Ultra-Relativistic Quantum Molecular Dynamics

• out-of-equilibrium transport model, (rel. Boltzmann equation)

• Particles interact via :

- measured and calculated cross sections

- string excitation and fragmentation

- formation and decay of resonances

• Provides full space-time dynamics of heavy-ion collisions


Why the HBT technique is important to probe the QGP?

Why the HBT technique is important to probe the QGP?

• We know, the transition can only take place in a very small space-time.

• Correlations of two final-state particles are closely linked to the space-time of the region of homogeneity (the relevant volume for particles of a given velocity, not the entire source, which can give partly the message of the source.

• A non-trivial structure in the excitation function of HBT might be seen IF there is a (phase) transition.


MotivationMotivation

At RHIC: look for signals of partonic matter. (large v2, mach cones, quenching,…)

At critRHIC/SPS:look for the mixed phase and the onset of deconfinement(long life times, large fluctuations, …)

E. Bratkovskaya, M.B. et al., PRC 2005


The promise…The promise…

• long life times in the mixed phase…

Rischke, Gyulassy, Nucl.Phys.A608:479-512,1996

~ Energy density

10 fold increase in life time during the mixed phase


Why use the UrQMD model?Why use the UrQMD model?

• Hydrodynamics failed to explain the decrease of HBT radii with kT (see, e.g. nucl-th/0305084)

• Might be due to the Corona effect at late stage?• Transport model, considering the full

rescattering process, might throw light on what other mechanisms generate the observed kT-dependence of the HBT radii


What’s the HBT technique?What’s the HBT technique?

32

3

31

3

32

31

6

),(

dp

Nd

dp

Nd

dpdp

Nd

KqC 21 ppq

2/)( 21 ppK

The quotient of two-particle and one-particle spectra

The two-particle correlator C(q,K) is related to the emission function S(x,K), Which is the Wigner phase-space density of the particle emitting system and can be viewed as the probability that a particle with average momentum K is emitted from the space-time point x in the collision region.

For identical bosons, 24

24

|),(|

|),(|1),(

KxSxd

eKxxSdKqC

xiq


Gaussian ParameterizationGaussian Parameterization

• To better understand the three-dimensional spatio-temporal source distribution. Although the realistic source deviates from a standard Gaussian, it provides the standard description of experimental data.

• There exist quite a few different types of Gaussian parameterization under different coordinate system (CMS, LCMS, YKP, etc…).

Nucl-ex/0505014

From one- to two- to three dimensional parameterization (e.g. nucl-th/0510049 for reviews)

Yano-Koonin parametrization


LCMS Gaussian ParameterizationLCMS Gaussian Parameterization

• Longitudinal co-moving system (out-side-long)

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

is the incoherence or chaoticity factor, lies between 0 (complete coherence) and ±1 (complete incoherence) in the real reactions. it will be affected by many factors other than the quantum statistics (bosons: 1, fermions: -1 ), for example, misidentified particles(contamination), the (long-lived) resonance, different technical details of Coulomb correctionsRL,O,S are B-P radii, Rol is the cross term and vanishes at mid-rapidity.


The out-side-long system sketchThe out-side-long system sketch

• Long: parallel to beam, and the longitudinal components of the pair velocity vanishes.(Kz=0)

• Side: perpendicular to beam and average pair momentum K.

• Out: perpendicular to Long and Side.

K

L

O

S

K

KqqO


The survey of Pratt radii RL,RO, and RS

The survey of Pratt radii RL,RO, and RS

• R~R(KT, Eb, b, (A,B), y, , (m1,m2))

Next, we show the results of the source of two negatively (except otherwise stated) charged pions using UrQMD model.

Quite a few model endeavors: Hydrodynamics models: matter in the collision region is taken as an ideal, locally thermalized fluid with the zero mean free path; (hydro+/PYTHIA+)UrQMD, RQMD: hadronic dynamics model with string degree of freedom. Having potentials for baryons at low beam energies. From UrQMD ver2.0, the PYTHIA (v6.1) was added in order to consider the hard process.MPC: Molnar’s Parton Cascade, (with the stiffest effective EoS)AMPT: A Multi-Phase Transport model (hadron+string+parton)HRM: Hadronic Rescattering Model (no strings/partons)etc…


How to calculate numerically?How to calculate numerically?

• Standard UrQMD (v2.2) output of freeze-out particles (http://www.th.physik.uni-frankfurt/~urqmd)

• CRAB (v3.0) used to analyze the (three-dimensional LOS) correlation of two identical particles.

(http://www.nscl.msu.edu/~pratt/freecodes/crab/home.html)

• Three-dimensional Gaussian fitting.

• Present study: pi-pi correlations


World HBT data 1World HBT data 1


World HBT data 2

World HBT data 2

• First (up to now only) systematic comparison between transport model (RQMD) and experimental data(Mike Lisa, 2005)


Systematic analysis is neededSystematic analysis is needed

• Hydro is known to fail for HBT radii

• Transport models can provide a baseline

Use UrQMD for a systematic study


Transverse momentumdependence of the HBT radii

at various energies


UrQMD vs. data @ AGSUrQMD vs. data @ AGS

02468

(6A

GeV

)(2

A G

eV

)(8

A G

eV

)(4

A G

eV

)

kT (MeV/c)

data: ; th: th.

Eb L O S

02468

(10.7

A G

eV

)

0 100 200 300 40002468

Ri (

fm)

0 100 200 300 400 0 100 200 300 400 500

02468

10

02468

<11%T

<5% T

2/)( 21 TTppKT

•Good agreement•Deviations at small kT for RL

and RS


The mass dependence of lifetime of resonances

The mass dependence of lifetime of resonances

The green lines:We consider the Mass dependenceOf lifetime of Resonances.

M

02468 fm

(6A

GeV

)(2

A G

eV)

(8A

GeV

)(4

A G

eV)

kT (MeV/c)

data: ; th: th.

Eb L O S

02468 fm

(10.

7A G

eV)

0 100 200 300 40002468 fm

Ri (

fm)

0 100 200 300 400 0 100 200 300 400 500

02468

10

fm

02468 fm

better agreement

Time from phase shift?


UrQMD @ SPS-NA49UrQMD @ SPS-NA49

<7.2% T

0 200 400

NA49 data: ; th:

0 200 400 0 200 400

s=0 fm/c

0 200 400 600

RS (fm

)R

O (fm

)

(20A GeV)

kT (MeV/c)

(40A GeV)(30A GeV) (80A GeV) (160A GeV)

RL (fm

)

0

2

4

6

8

10

0

2

4

6

8

0 200 4000

2

4

6

8

Note the effect of short formation times: more early pressure


UrQMD @ SPS-CERESUrQMD @ SPS-CERES

<5% T

0

2

4

6

8

10CERES data: ; th:

0

2

4

6

8

0 200 4000

2

4

6

8

0 200 400 0 200 400 600

RS (fm

)R

O (fm

)

kT (MeV/c)

(40A GeV) (80A GeV) (160A GeV)

RL (fm

)


[email protected]@RHIC

0

2

4

6

8

10

15%T

0

2

4

6

8

exp.: ; th.:

0

2

4

6

8

0 200 400 600 8000

2

4

6

8

kT (MeV/c)

O SL

(62.

4 G

eV)

(30

GeV

)(1

30 G

eV)

sNN

(200

GeV

)

Ri (

fm)

0 200 400 600 800 0 200 400 600 800

<15% T

<15% T

<10% T

<5% T

Deviation for RO!


R.vs.b@RHIC GeVR.vs.b@RHIC GeV200s

0

5

10

15

20

25

RO (fm

)

th. exp. 0-5% 10-20% 30-50% 50-80%

+15 fm

+10 fm

+5 fm

+0 fm

100 200 300 400 500 6000

5

10

15

20

RS (fm

)

+15 fm

+10 fm

+5 fm

+0 fm

200 300 400 500 600

RL (fm

)

+15 fm

+10 fm

+5 fm

+0 fm

kT (MeV/c)

RO problems grow towards centralcollisions.

lines shifted by 5 fm each


-correlations at RHIC-correlations at RHICQ

. Li

, M

.B.,

H.

Sto

ecke

r, n

ucl-

th/0

602

032;

D

ata:

ST

AR

• Correlations are well described except for most central reactions


The HBT puzzle? The HBT puzzle?

• Model calculations of RO/RS or (RO2-RS

2)1/2 are usually larger than the experimental data

Duration time (in the absence of flow):

2

22 )(

SO RR

No indication of long life time in the data

1 10 100 1000 100000

2

4

6

8

(R2 O-R

2 S)1/

2 (fm

)

Eb (A GeV)

Circles: kT=100 MeV/c

Squares: kT=200 MeV/c

Stars: exp. data

Li, Bleicher, Stoecker, arXiv:0706.2091. JPG in press


The (argued) ‘disadvantages’ in the UrQMD calculations

The (argued) ‘disadvantages’ in the UrQMD calculations

• Hadronic potentials for baryons in the above calculations.

• No string-string interaction although the string degree of freedom exists.

• Or, no deconfined quarks nor gluons and the interactions between them.


More collisions by setting zero formation time for strings

More collisions by setting zero formation time for strings

The difference BetweenC(qo) and C(qs)almost disappearsafter consideringzero formation timefor string.

It is very time consuminge.g. :SPS-E160:3events/hRHIC-s200:1event/d

A larger early pressure especially in the sideward direction leads to larger Rs


Ro/Rs at SPS(Eb=160 A GeV)

Ro/Rs at SPS(Eb=160 A GeV)

Zero-formation time

Leads to much smaller

Ro/Rs ratio mainly due to a larger Rs.

0 100 200 300 400 500 6000

2

4

6

8

10

(R

O

2 -RS

2 )1/2 (

fm)

kT (MeV/c)

NA49 data CERES data default

s=0 fm/c

Eb=160A GeV

Early stage,Early state!


At RHIC: How about other approaches?

At RHIC: How about other approaches?

From nucl-ex/0505014 byM. Lisa

AMPT:HBT is sensitive to The parton-scatteringCross sections.

HRM: considering onlythe hadron rescattering(with sudden collisions ),No parton degree of freedom


How to solve the HBT puzzleHow to solve the HBT puzzle

• reduce (or 0) string formation time for more pressure? (tremendous number of collisions make it almost impossible to calculate the HBT interferometry at RHIC) the idea in HRM and checked for elliptic flow and HBT at SPS in UrQMD• consider Partons? the idea in AMPT Not yet in UrQMD model

with the help of another model: qMD,

• consider optical potential for pions (chiral symmetry) see PRL94, 102302(2005), PRC73, 024901(2006)

and, hadronic potential should be also paid attention.


Rapidity studies


[email protected]@NA49

Weak y-dependencein all HBT radiiFor RS, it decreases slowly with rapidity.

NA49 data For kT<100 MeV/c

Weak y-dep, Why? strong x-p correlation

good agreement


Possible reason…Possible reason…

-2 -1 0 1 2

2

4

6

8

10

(NB

* ->X / N

Strin

g->X)

free

ze-o

ut

Ycm

Eb (A GeV)

20 40 160

kT<100 MeV/c

Different particle sources as function of rapidity: Direct production vs. decay


Energy dependence


R.vs.Eb

@small KT

R.vs.Eb

@small KT

• Overall reasonable agreement

• But, Ro/Rs too big

• Difference between CERES and NA49 (acceptance?)

1 10 100 1000 100000

2

4

6

8

0

2

4

6

8

0

2

4

6

8

10R

L (fm

)

Eb (A GeV)

exp (stars):k

T~150: E2,4,6,8,

E20,30,40,80,160 (NA49)k

T~170: s130

kT~200: E10.7,s62.4,s200

E40,80,160 (CERES)

Ro (fm

) R

s (fm

)




Mean free pathMean free path

• UrQMD seems to supports the finding of a (nearly) constant mfp.

• However, this is surprising within a microscopic analysis (here one expects mfp ~ R ~ 5 fm)

22/32 SLf RRV


Droplets: > 10-100 (Mishustin)

Taken from a talk by B. Lungwitz at CPOD 2007

UrQMD data from Lungwitz& Bleicher, arXiv:0707.1788


Summary and outlookSummary and outlook

• Good (quantitatively) agreement of the calculated HBT radii with data from AGS to RHIC.

• The decay of resonances affects the HBT radii (mainly at low kT).

• HBT puzzle is also seen by the comparison of our calculations with data, especially at RHIC energies (flow and HBT puzzles are twin.)

It seems essential to consider the interactions between new degrees of freedom.

1 10 100 1000 100000

2

4

6

8

(R2 O-R

2 S)1/

2 (fm

)

Eb (A GeV)



Stars: exp. data

Where are all the irregular structures expected when entering the mixed phase?

HBT results from UrQMD

Documents

hbt radiimarcus bleicher

outlookmarcus bleicher

mixed phasemarcus bleicher

hbt technique

ion collisionsmarcus

hbt puzzlesummary

hbt results

excitation function