Olena LinnykOlena Linnyk

Charm dynamics from transport calculations

Symposium and 10th CBM Collaboration MeetingSeptember 25 – 28, 2007

Introduction

FAIR energiesFAIR energies are well suited to study are well suited to study dense and hot nuclear matterdense and hot nuclear matter – – a phase transition to QGP ,a phase transition to QGP , chiral symmetry restoration, chiral symmetry restoration, in-medium effectsin-medium effects

Observables for CBM:Observables for CBM: Excitation function of Excitation function of

particle yields and ratiosparticle yields and ratios Transverse mass spectraTransverse mass spectra Collective flowCollective flow DileptonsDileptons Open and hidden charm Open and hidden charm Fluctuations and Fluctuations and

correlationscorrelations ......

Way to study:Way to study:Experimental Experimental energy scanenergy scan of of different different observablesobservables in order to in order to find an find an ‚anomalous‘‚anomalous‘ behavior in behavior in comparison with comparison with theorytheory

Microscopic transport modelsMicroscopic transport models

• Strangeness enhancement Strangeness enhancement • Multi-strange particle enhancementMulti-strange particle enhancement• Charm suppressionCharm suppression• Collective flow (vCollective flow (v11, v, v22))• Thermal dileptonsThermal dileptons• Jet quenching and angular correlationsJet quenching and angular correlations• High pHigh pTT suppression of hadrons suppression of hadrons• Nonstatistical event by event fluctuations and correlations Nonstatistical event by event fluctuations and correlations • ... ...

Experiment: Experiment: measures final hadrons and leptonsmeasures final hadrons and leptons

Signals of the phase transition:Signals of the phase transition:

How to learn about physics from data?How to learn about physics from data?

Compare with theory! Compare with theory!

Models for heavy ion collisions

Microscopical transport models provide the dynamical Microscopical transport models provide the dynamical description of description of nonequilibriumnonequilibrium effects in heavy-ion collisions effects in heavy-ion collisions

Thermal modelsThermal models

Hydro models (local equilibrium)Hydro models (local equilibrium)

Transport modelsTransport models

Freeze-out

Initial State

Au

Au

Hadronization

Quark-Gluon-Plasma ?

time

Basic concepts of Hadron-String Dynamics

• for each particle species i (i = N, R, Y, , , K, …) the phase-space density fi

follows the transport equations

with the collision terms Icoll describing: elastic and inelastic hadronic reactions formation and decay of baryonic and mesonic resonances string formation and decay (for inclusive production: BB(for inclusive production: BBXX, mB, mBXX, , XX =many particles) =many particles)

• Implementation of detailed balance on the level of 12 and 22 reactions (+ 2n multi-meson fusion reactions)

• Off-shell dynamics for short living states

BB BB B´B´, BB B´B´, BB B´B´m, mB B´B´m, mB m´B´, mB m´B´, mB BB´́

),...,f,f(fI,t)p,r(fHHt M21colliprrp

• hadrons - baryons and mesons including excited states (resonances)

• strings – excited colour singlet states (qq - q) or (q – qbar)

Based on the LUND string model

& perturbative QCD via PYTHIA

• leading quarks (q, qbar) & diquarks

(q-q, qbar-qbar)

NOT included in the transport models presented here :o no explicit parton-parton interactions (i.e. between quarks and gluons) outside

strings!o no QCD EoS for partonic phase under construction: PHSD – Parton-Hadron-String-Dynamics W. Cassing arXiv:0704.1410

Degrees of freedom in HSD

pre-hadronspre-hadrons

F

__

qqq

time

color electricfield

z

Time evolution of the energy density

HSD HSD transport model allows to calculate the energy momentum tensor Ttransport model allows to calculate the energy momentum tensor T(x) for all (x) for all space-time points x and thus the energy density space-time points x and thus the energy density (r,t) which is identified with T(r,t) which is identified with T0000(r,t)(r,t)

Local energy density vs Bjorken energy density Bj

• transient time for central Au+Au at 200 GeV:transient time for central Au+Au at 200 GeV: ttrr ~ 2R~ 2RAA//cmcm ~ 0.13 fm/c ~ 0.13 fm/c

• cc formation time: cc formation time: CC ~ 1/M~ 1/MT T ~ ~ 1/4GeV ~ 0.05 fm/c < 1/4GeV ~ 0.05 fm/c < ttrr

• cc pairs are produced in the cc pairs are produced in the initial hard NNinitial hard NN collisions collisions in time period in time period ttrr

0 100 200 300 4000

1

2

3

4

5

0 100 200 300 4000

1

2

3

4

5

6

7

PHENIX HSD

Au+Au, 200 GeV

dE

T/d/

0.5N

part [

GeV

]

Npart

PHENIX HSD

Au+Au, 200 GeV

B

j* [

GeV

/fm

2 /c]

Npart

dy

dE

τA

1ε T

Bj

Bjorken energy density:Bjorken energy density:

JJ

cc

‚‚

at RHICat RHIC BjBj ~ 5 GeV/fm~ 5 GeV/fm22/c/c

AAis the nuclei transverse overlap areais the nuclei transverse overlap area is the formation time of the mediumis the formation time of the medium

‚‚Local‘ energy densityLocal‘ energy densityduring during

transient time transient time ttrr GeV/fmGeV/fm22/c] / [0.13 fm/c]/c] / [0.13 fm/c] ~ 30 GeV/fm~ 30 GeV/fm33

accounting accounting CC : :~ 28 GeV/fm~ 28 GeV/fm33

HSD reproduces PHENIX data for Bjorken energy density very wellHSD reproduces PHENIX data for Bjorken energy density very well HSD results are consistent with simple estimates for the energy density HSD results are consistent with simple estimates for the energy density

Charmonium production in pN

J/exp = J/ + B(cJ/) c + B(´->J/) ´

1 0 1 001 0-1

1 00

1 01

1 02

1 03

1 04

1 05

1 06

1 07

J /

/

p + N D + D b a r

(s)

[nb]

s1 /2 [G eV ]

Hard probe binary scaling!

(J/) and(‘ ):parametrization of the

available experimental data

But data close to But data close to thresholdthreshold

are still needed ! are still needed ! FAIR at GSIFAIR at GSI

Charmonium production in pN

-4 -2 0 2 40

20

40

60

PHENIX HSD scaled with cross section ratio

pp->J/+X, s1/2=200 GeV

Br

d/d

y [n

b]

Differential cross section of charm production is successfully parametrized, too

Charmonium production vs absorption

Charmonium is absorbed by

Scattering on nucleons (normal nuclear absorption, as in pA) Interaction with secondary hadrons (comovers) Dissociation in the deconfined medium (suppression in QGP)

DD

DDbarbar

J/J/

CC

‘‘

Charm sector reflects the dynamics in the early phase of heavy-ion collisions !

Anomalous J/ suppression

0 100 200 300 4000

10

20

30

40

.

Pb+Pb, 158 A GeV

Npart

Baryon absorption Glauber model NA50 2004

J/ ‚normal‘ absorption by nucleons (Glauber model)

Experimental observation Experimental observation (NA38/50/60):(NA38/50/60):extra suppression in A+A collisions; increasing with centrality

Scenarios for anomalous charmonium suppression

• QGP colour screening

[Digal, Fortunato, Satz ’03]• Comover absorption

[Gavin & Vogt, Capella et al.`97] absorption by low energy inelastic scattering with ‚comoving‘ mesons (m=,,,...)

J/

C melting

0 20 40 60 80 100 120 1400

10

20

30

40

50

NA50 (2000):anal. Aanal. Banal. C

HSD UrQMD

B(

J/)

/(D

Y)| 2.

9-4.

5

Pb+Pb, 160 A GeV

ET [GeV]

J/+m D+Dbar

´ +m D+Dbar

C +m D+DbarDissociation energy density Dissociation energy density d d ~ 2(T~ 2(Tdd/T/Tcc))44

Quarkonium dissociation T:Quarkonium dissociation T:

4.0 4.5 5.0 5.510

-1

100

101

J/+K*

J/+K

J/+

J/+

[m

b]

s1/2

[GeV]

• Phase-space model for charmonium + meson dissociation:

[PRC 67 (2003) 054903][PRC 67 (2003) 054903]

2. J/ recombination cross sections by D+Dbar annihilation: D+Dbar -> J/(c,‘) + meson (, K , K*) are determined by detailed balance!

4.0 4.5 5.0 5.5100

101

s1/2 [GeV]

D*+Dbar*

D+Dbar*, D*+Dbar

D+Dbar

[m

b]

20

2

Ψ

2χ

2J/Ψ

'C

6

432i

43214isospin4321

|M||M||M||M|

ΨJ/Ψ,χi

s

mm|M|

s

EEEE2gsσ

'C

,

constant matrix elementconstant matrix element

1. Charmonia dissociation cross sections with , K and K* mesons J/(c,‘) + meson (, K , K*) <-> D+Dbar

Modelling the comovercomover scenario in HSD

Charmonium recombination by DDbar annihilation

5 10 15 20

10-8

10-7

10-6

10-5

10-4

10-3

time [fm/c]

J/+m->D+Dbar D+Dbar->J/+m

Pb+Pb, s1/2=17.3 GeV, central

dN

/dt

At SPS recreation of J/ by D-Dbar annihilation is negligible

5 10 15 20

10-4

10-3

10-2

10-1

time [fm/c]

J/+m->D+Dbar D+Dbar->J/+m

Au+Au, s1/2

=200 GeV, central

dN

/dt

But at RHIC recreation of J/ by D-Dbar annihilation is strong!

NNDDDD~16~16

[OL et al., nucl-th/0612049, NPA 786 (2007) 183 ][OL et al., nucl-th/0612049, NPA 786 (2007) 183 ]

Threshold energy densities:

J melting: (J )=16 GeV/fm3

c melting:(c ) =2 GeV/fm3

‚melting:( ‚) =2 GeV/fm3

0

5

10

15

1

2

3

4

5

-10-5

05

10

Pb+Pb, 160 A GeVb=1 fm

Energy density (x=0,y=0,z;t) from HSD

Modeling the QGP meltingQGP melting in HSD

Comparison to data at SPS energy

Pb+Pb and In+In @ 158 A GeV comover absorptioncomover absorption

[OL et al NPA786 (2007) 183]

Pb+Pb and In+In @ 160 A GeV consistent with the comover absorption

for the same parameter set!

0 25 50 75 100 125 150

0 50 100 150 2000

10

20

30

40

0 100 200 300 400

HSD

NA50 1997 NA50 1998-2000 Baryon absorption Comover absorption

ET [GeV]

0 50 100 150 2000.000

0.005

0.010

0.015

HSD

Baryon absorption Comover absorption

B

(')

' /

B

(J/

) J/

Npart

HSD

In+In, 158 A GeV

B(

J/)

/(D

Y)| 2.

9-4.

5

Npart

NA60 2005 Glauber model Baryon absoprtion Comover absorption .

HSD

Pb+Pb, 158 A GeV

Npart

NA50 2004 Glauber model Baryon absorption Comover absorption

0 50 100 150 200 250 300 350 4000.4

0.6

0.8

1.0

1.2

NA60, In+In, 158 A GeV (2007)HSD

NA60, In+In, 158 A GeV Comover absorption NA50, Pb+Pb, 158 A GeV Comover absorption

((J

/)/(

DY

)) /

((J

/)/(

DY

))G

laub

er

Npart

Pb+Pb and In+In @ 158 A GeV QGP threshold meltingthreshold melting

´ absorption too strong, which contradict data

[OL et al NPA786 (2007) 183]

0 25 50 75 100 125 150

0 50 100 150 2000

10

20

30

40

0 100 200 300 400

HSD

NA50 1997 NA50 1998-2000 QGP threshold melting

J/=16, c

=2, '=2 GeV/fm3

ET [GeV]

0 50 100 150 2000.000

0.005

0.010

0.015

HSD

QGP threshold melting

J/=16, c

=2, '=2 GeV/fm3

B

(')

' /

B

(J/

) J/

Npart

HSD

In+In, 158 A GeV

B(

J/

)/(

DY

)| 2.9-

4.5

Npart

NA60 2005 QGP threshold melting

J/=16, c

=2, '=2 GeV/fm3

HSD

Pb+Pb, 158 A GeV

Npart

NA50 2004 QGP threshold melting

J/=16, c

=2, '=2 GeV/fm3

0 50 100 150 200 250 300 350 4000.4

0.6

0.8

1.0

1.2

NA60, In+In, 158 A GeV (2007)HSD

NA60, In+In, 158 A GeV QGP threshold melting NA50, Pb+Pb, 158 A GeV QGP threshold melting

((J

/)/(

DY

)) /

((J

/)/(

DY

))G

laub

er

Npart

(J )=16 GeV/fm3, (c ) =( ‚) =2 GeV/fm3

• Set 2:Set 2: an increase of the an increase of the melting energy density melting energy density

(( ‚‚) =6.55 GeV/fm) =6.55 GeV/fm33

reduces the reduces the ‚‚ suppression, suppression, but contradicts LQCD but contradicts LQCD predictions for predictions for

TTdd(( ‚‚) ~ 1.2 T) ~ 1.2 TCC! !

[OL et al., nucl-th/0612049, NPA07][OL et al., nucl-th/0612049, NPA07]

(J(J )=16 GeV/fm)=16 GeV/fm33, , ((c c ) =2 GeV/fm) =2 GeV/fm33, ,

(( ‚‚) =6.55 GeV/fm) =6.55 GeV/fm33

´ data contradict threshold melting scenario with lQCD d

0 25 50 75 100 125 1500.000

0.005

0.010

0.015 NA50 1997 NA50 1998-2000 Comover absorption QGP threshold melting:

J/=16,

c

=2, '=2 GeV/fm3

J/=16,

c

=2, '=6.55 GeV/fm3

B

(')

' /

B

(J/

) J/

Pb+Pb, 158 A GeV

HSD

ET [GeV]

Comparison to data at RHIC energy

R. Rapp et al.PRL 92, 212301 (2004)R. Rapp et al.PRL 92, 212301 (2004) R. Thews et al, Eur. Phys. J C43, 97 (2005)R. Thews et al, Eur. Phys. J C43, 97 (2005)

Yan, Zhuang, Xu, Yan, Zhuang, Xu, PRL97, 232301 (2006)PRL97, 232301 (2006) Bratkovskaya et al., PRC 69, 054903 (2004)Bratkovskaya et al., PRC 69, 054903 (2004)

A. Andronic et al., NPA789, 334 (2007) A. Andronic et al., NPA789, 334 (2007)

R. Rapp et al.PRL 92, 212301 (2004)R. Rapp et al.PRL 92, 212301 (2004) R. Thews et al, Eur. Phys. J C43, 97 (2005)R. Thews et al, Eur. Phys. J C43, 97 (2005)

Yan, Zhuang, Xu, Yan, Zhuang, Xu, PRL97, 232301 (2006)PRL97, 232301 (2006) Bratkovskaya et al., PRC 69, 054903 (2004)Bratkovskaya et al., PRC 69, 054903 (2004)

A. Andronic et al., NPA789, 334 (2007) A. Andronic et al., NPA789, 334 (2007)

Comover absorption + regenerationComover absorption + regeneration

A successful prediction

HSDHSD

obtained assumingthe existance of comovers throghout the collision, i.e. at all energy densities.

NB:NB:

Regeneration is essential!

Au+Au @ s1/2=200 GeV Comover absorption + Comover absorption +

regenerationregeneration

[OL et al arXiv:0705.4443]

In comover scenario, suppression atmid-ymid-y stronger than atforward yforward y,unlike the data

0.0

0.5

1.0

HSD |y|<0.35 1.2<|y|<2.2

RA

A(J

/)

PHENIX, |y|<0.35 PHENIX, 1.2<|y|<2.2

Au+Au, s=200 GeV, comover absorption

0 100 200 300

0.000

0.005

0.010

0.015

D+Dbar J/ +m

B

(')

'

/ B

(J/

) J/

Npart

0 100 200 300

D+Dbar J/ +m

+ cut

=1 GeV/fm3

Npart

Space for parton phase effects

Energy density cut cut=1 GeV/fm3 reduces

the meson comover absorption

0.0

0.5

1.0

HSD |y|<0.35 1.2<|y|<2.2

RA

A(J

/)

PHENIX, |y|<0.35 PHENIX, 1.2<|y|<2.2

+ recombinationD+Dbar J/ +m

without recombination

0.0

0.5

1.0

+ recombinationD+Dbar J/ +m

+ cut

=1 GeV/fm3

Au+Au, s=200 GeV, QGP threshold scenario

0 100 200 300

0.000

0.005

0.010

0.015

B

(')

'

/ B

(J/

) J/

Npart

0 100 200 300

Npart

0 100 200 300 400

0.000

0.005

0.010

0.015

Npart

Au+Au @ s1/2=200 GeV Threshold meltingThreshold melting

Satz’s model: complete dissociation of Satz’s model: complete dissociation of initial J/initial J/and and ´ due to the very large ´ due to the very large local energy densities ! local energy densities !

Charmonia recombination Charmonia recombination is important!is important!

Energy density cut Energy density cut cutcut=1 GeV/fm=1 GeV/fm33 reduces the reduces the meson comover absorption, however, D+Dbar meson comover absorption, however, D+Dbar

annihilation can not generate enough charmonia,annihilation can not generate enough charmonia,especially for peripheral collisions! especially for peripheral collisions!

QGP threshold melting scenario is ruled out by PHENIX data!QGP threshold melting scenario is ruled out by PHENIX data!

-3 -2 -1 0 1 2 310-5

10-4

10-3

threshold melting +energy cut comover absorption +energy cut

QGP no cut comover no cut

PHENIXHSD centralB

dN

(J/

)/d

y

y

Au+Au, s=200 GeV

0 50 100 150 200 250 300 350 4000.0

0.5

1.0

1.5

2.0

2.5Au+Au, s1/2=200 GeV

HSD

RA

A(f

orw

ard

y)

/ RA

A(m

id-y

)

Npart

PHENIX threshold melting comover absorption

both with recombination (D+Dbar)

Rapidity !

HSD predictions for FAIR energy

Huge energy density is reached ( >crit=1 GeV/fm3) also at FAIR (> 5 A GeV).

Addtionally, high baryon density.

Energy density at FAIR

J/J/ excitation function

ComoverComover reactions in the hadronic phase give almost a constant suppression;

pre-hadronic reactions lead to a larger recreation of charmonia with Ebeam .

100 1000 100000.0

0.2

0.4

0.6

0.8

1.0

Central

S

Ebeam

, A GeV

Comover + cut

Comover

QGP + cut

QGP

100 1000 100000.0

0.2

0.4

0.6

0.8

1.0

Minimum bias

HSD

SE

beam, A GeV

The J/ melting scenariomelting scenario with hadronic comover recreation shows a maximum maximum suppressionsuppression at Ebeam = 1 A TeV; exp. data ? exp. data ?

´́ excitation function

100 1000 100000.000

0.004

0.008

0.012

Central

B

( ')

'

/ B

(J/

) J/

Ebeam

, A GeV

Comover+cut

Comover

QGP+cut

QGP

100 1000 10000

Minimum bias

HSD

' to J/ ratio

Ebeam

, A GeV

Different scenarios can be distinguished at FAIR energies: ComoverComover scenario predicts a smooth excitation function whereas the

‘threshold meltingthreshold melting’ shows a step in the excitation function

Predictions for J/Predictions for J/and and ´ suppression in ´ suppression in Au+Au at Au+Au at CBMCBMPredictions for J/Predictions for J/and and ´ suppression in ´ suppression in Au+Au at Au+Au at CBMCBM

Possible mechanisms can be disentangled:

´/(J/ is lower in the ‚comover absorption‘ since the average comover density decreases

only moderately with lower bombarding energy whereas the energy density falls rapidly [OL et al., nucl-th/0612049, NPA07][OL et al., nucl-th/0612049, NPA07]

0 50 100 150 200 250 300 350 4000.0

0.2

0.4

0.6

0.8

1.0

HSD

S(J/)

Npart

Baryon absorption Comover absorption QGP threshold melting

J/=16,

c

=2, '=6.55 GeV/fm3

0 50 100 150 200 250 300 350 4000.000

0.002

0.004

0.006

Au+Au, 25 A GeV

HSD

Comover absorption QGP threshold melting

J/=16,

c

=2, '=6.55 GeV/fm3

QGP threshold melting

J/=16,

c

=2, '=2 GeV/fm3

B

(')

' /

B

(J/

) J/

Npart

HSD: vHSD: v22 of D+Dbar and J/ of D+Dbar and J/ from Au+Au versus p from Au+Au versus pTT and and y at RHICy at RHIC HSD: vHSD: v22 of D+Dbar and J/ of D+Dbar and J/ from Au+Au versus p from Au+Au versus pTT and and y at RHICy at RHIC

• HSD:HSD: D-mesons and J/D-mesons and J/follow the follow the charged particle flow charged particle flow small vsmall v2 2 < 3%< 3%

• Exp. data at RHICExp. data at RHIC show show largelarge collective collective flow of D-mesons up to flow of D-mesons up to vv22~10%!~10%!

=> strong initial flow of => strong initial flow of non-hadronic nature!non-hadronic nature!

-6 -4 -2 0 2 4 60.00

0.01

0.02

0.03

0.04

0.05

0.06

PHOBOS HSD

Au+Au, s1/2

=200 GeVcharge particles

v 2()

-2 -1 0 1 2

-0.02

0.00

0.02

0.04

0.06Au+Au, s1/2=200 GeV

b=7 fm

v 2 (y

)

D+Dbar J/

y

Collective flow Collective flow from from hadronic hadronic interactionsinteractions is is too low at too low at midrapidity !midrapidity !

[E. Bratkovskaya et al PRC 71 (2005) 044901][E. Bratkovskaya et al PRC 71 (2005) 044901]

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-0.05

0.00

0.05

0.10

0.15

0.20

Au+Au, s1/2=200 GeVb=7 fm, 0<y<1

v 2 (p T

)

PHENIX D+Dbar J/

pT [GeV/c]

HSD predictions for CBMCBM elliptic flow at 25 A GeV

Challenge for CBM!Challenge for CBM!

0.0 0.5 1.0 1.5 2.0-0.05

0.00

0.05

0.10

0.15

0.20

v 2

Au+Au, 25 A GeV b=7 fm, |y|<1

charged hadrons D+Dbar

HSD

pT [GeV/c]

•HSD:HSD: D-mesons and D-mesons and J/J/follow the charged particle follow the charged particle

flow flow small vsmall v2 2

Possible observation at CBM:Possible observation at CBM: strong initial flow of D-mesons strong initial flow of D-mesons and J/and J/ due to partonic due to partonic interactions!interactions!

J/ probes early stages of fireball and HSD is the tool to model it.

Comover absorption and threshold melting both reproduce J/ survival in Pb+Pb as well as in In+In @ 158 A GeV, while ´ data are in conflict with the melting scenario.

Comover absorption and colour screening fail to describe Au+Au at s1/2=200 GeV at mid- and forward rapidities simultaneously.

Deconfined phase is clearly reached at RHIC, but a theory having the relevant/proper degrees of freedom in this regime is needed to study its properties (PHSD).

PHSD - PHSD - transport description of the partonic and hadronic phasestransport description of the partonic and hadronic phases

Non-equilibrium -> full evolution of the collision

Universality-> large range of s1/2 from one code -> predictions -> exitation functions

High presicion-> distinguish physical mechanisms-> possibility of verification by exp

Transport aproach (HSD, UrQMD, ...)