Convenors: Convenors: EElenalena Bratkovskaya Bratkovskaya**, C, Christianhristian Fuchs, B Fuchs, Burkhardurkhard Kämpfer Kämpfer

*FIAS, J.W. Goethe *FIAS, J.W. Goethe UniversitätUniversität,, Frankfurt am MainFrankfurt am Main

29.05.2006 , CBM Workshop29.05.2006 , CBM Workshop „ „ The Physics of High Baryon Density The Physics of High Baryon Density „„

Status Physics Book:Status Physics Book: Observables and PredictionsObservables and Predictions

1.1. IntroductionIntroduction2.2. Excitation function of particle yields Excitation function of particle yields

and ratiosand ratios3.3. Transverse mass spectraTransverse mass spectra4.4. Collective flowCollective flow5.5. DileptonsDileptons6.6. Open and hidden charm Open and hidden charm 7.7. Fluctuations and correlationsFluctuations and correlations

Content of the Chapter:Content of the Chapter: Observables and PredictionsObservables and Predictions

based on dynamical models – transport based on dynamical models – transport approaches and hydrodynamicsapproaches and hydrodynamics

Concentrate on FAIR energy range 10-30 A GeVConcentrate on FAIR energy range 10-30 A GeV

1. 1. IntroductionIntroduction

FAIR energiesFAIR energies are well suited to study are well suited to studydense 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

(cf. talk by J. Randrup)(cf. talk by J. Randrup)

Way to study:Way to study:Experimental Experimental energy scanenergy scan of different of different observables in order to find an observables in order to find an ‚anomalous‘‚anomalous‘ behavior by comparing with theorybehavior by comparing with theory

2. 2. Excitation function of particle yields and Excitation function of particle yields and ratiosratios

AGSNA49 BRAHMS

10-1 100 101 102 103 10410-6

10-4

10-2

100

102

104

AGS SPS RHIC HSD ' 99

__

D(c)

J/D(c)

KK+

+

Mul

tipl

icit

y

Au+Au (central)

Energy [A GeV]

Overview on the experimantal Overview on the experimantal meson and meson and strange baryon abundanciesstrange baryon abundancies from central from central Au+Au/Pb+Pb collisions versus s Au+Au/Pb+Pb collisions versus s 1/21/2

2. 2. Excitation function of particle yields and ratiosExcitation function of particle yields and ratios

100 101 102 103 1040.00

0.05

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100 101 102 103 1040.00

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100 101 102 103 1040.00

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0.04

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0.08

HSD UrQMD GiBUU

y=0

E866 NA49 PHENIX STAR BRAHMS, 5% BRAHMS, 10%

K+/+

Rat

ios

<K+>/<+> 4

E866 NA49 BRAHMS, 5%

HSD UrQMD

Elab

/A [GeV]

E866 NA49 PHENIX STAR BRAHMS, 5% BRAHMS, 10%

K/

E866 NA49 BRAHMS, 5%

<K>/<>

E877 NA49 STAR

(+0) /

E877 NA49

<+0>/<>

Elab

/A [GeV]

Transport models: Transport models: HSD, UrQMD, GiBUUHSD, UrQMD, GiBUU

Exp. data are not well reproduced Exp. data are not well reproduced within the hadron-string picture => within the hadron-string picture => evidence forevidence for nonhadronic degrees of nonhadronic degrees of freedomfreedom

3. 3. Transverse mass spectraTransverse mass spectra

Transport models: Transport models: • HSD 2.0 (+ Cronin effect)HSD 2.0 (+ Cronin effect)

• UrQMD 2.0 UrQMD 2.0 UrQMD 2.2 (effective heavy resonances with UrQMD 2.2 (effective heavy resonances with masses masses 2 < M < 32 < M < 3 GeV and isotropic decay) GeV and isotropic decay)

• GiBUUGiBUU

All transport models fail to reproduce the T-All transport models fail to reproduce the T-slope without introducing special „tricks“ slope without introducing special „tricks“ which are, however, which are, however, inconsistentinconsistent with other with other observables!observables!

10 1000.10

0.15

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0.25

0.30

0.35

10 1000.10

0.15

0.20

0.25

0.30

0.35

T [

GeV

]

E866 NA49 NA44 STAR BRAHMS PHENIX

Au+Au / Pb+Pb -> K++X

T [

GeV

]

HSD HSD with Cronin eff. UrQMD 2.0, 2.1 GiBUU 3f-hydro

E866 NA49 NA44 STAR BRAHMS PHENIX

HSD HSD with Cronin eff. UrQMD 2.0, 2.1 3f-hydro

Au+Au / Pb+Pb -> K+X

s1/2 [GeV]

3D-fluid hydrodynamical model 3D-fluid hydrodynamical model gives the right slope!gives the right slope!Is the matter a parton liquid?Is the matter a parton liquid?

4. 4. Collective flow: general considerationsCollective flow: general considerations 4. 4. Collective flow: general considerationsCollective flow: general considerations

22

22

yx

yx2

T

x1

21TTTT

pp

ppv

p

pv

...)cos(22v)cos(2v12π

1

dpdyp

dN

ddpdyp

dN

v2 = 7%, v1=0

v2 = 7%, v1=-7%

v2 = -7%, v1=0

Ou

t-of

-pla

ne

In-plane

Y

X

- - directed flowdirected flow

- - elliptic flow elliptic flow

VV2 2 > 0 > 0 indicates indicates in-planein-plane emission of particles emission of particles

VV2 2 < 0 < 0 corresponds to a corresponds to a squeeze-out squeeze-out perpendicular perpendicular

to the reaction plane (to the reaction plane (out-of-planeout-of-plane emission) emission)

x

zNon central Au+Au collisions : interaction between constituents leads to apressure gradient => spatial asymmetry is converted to an asymmetry in momentum space => collective flow

Y

4. 4. Collective flow: vCollective flow: v22 excitation function excitation function

Proton vProton v22 at at low energylow energy shows sensitivity to the shows sensitivity to the nucleon potentialnucleon potential.. Cascade Cascade codes fail to describe the exp. data.codes fail to describe the exp. data. AGSAGS energies: energies: transitiontransition from squeeze-out to in-plane elliptic flow from squeeze-out to in-plane elliptic flow

0.1 1 10

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

RBUU (Munich), potential RBUU (Giessen), potential RBUU (Giessen), cascadeGiBUU, potentialGBUU, cascade

Au+Au, mid-rapidity, semi-centralprotons

EOS/ E895/ E877 FOPI/ Plastic Ball/ LAND/ MSU

v 2

Ebeam

[GeV]

4. 4. Collective flow: vCollective flow: v22 excitation functions excitation functions

vv2 2 excitation functions from string-hadronic transport models excitation functions from string-hadronic transport models – UrQMD: – UrQMD:

4. 4. Collective flow: vCollective flow: v11 excitation functions excitation functions

2+1 fluid Hydro (Frankfurt) predicts 2+1 fluid Hydro (Frankfurt) predicts „antiflow“ of protons„antiflow“ of protons – if the matter undergoes a – if the matter undergoes a 1st order phase transition to the QGP1st order phase transition to the QGP

Warning: Warning: other Hydro models don‘t show such other Hydro models don‘t show such „antiflow“ => Hydro results are very sensitive to „antiflow“ => Hydro results are very sensitive to the initial and „freeze-out“ conditions! the initial and „freeze-out“ conditions!

2+1 fluid Hydro2+1 fluid Hydro

PT – phase transitionPT – phase transitionMPM – mixed phase EoSMPM – mixed phase EoS1F,2F,3F –1,2,3 fluid hydro1F,2F,3F –1,2,3 fluid hydro(Ivanov et al.)(Ivanov et al.)

Directed flow vDirected flow v1 1 & elliptic flow v& elliptic flow v2 2 for Pb+Pb at 40 A GeVfor Pb+Pb at 40 A GeVDirected flow vDirected flow v1 1 & elliptic flow v& elliptic flow v2 2 for Pb+Pb at 40 A GeVfor Pb+Pb at 40 A GeV

•Small wiggle in vSmall wiggle in v11 at at

midrapidity not described by midrapidity not described by

HSD, UrQMD and 3-fluid HSD, UrQMD and 3-fluid

hydro hydro

•Too large Too large elliptic flow velliptic flow v22 at at

midrapidity from HSD, midrapidity from HSD,

UrQMD and 3-fluid hydro for UrQMD and 3-fluid hydro for

all centralities !all centralities !

Experimentally: Experimentally:

breakdown of breakdown of vv22 atat

midrapidity !midrapidity !

Signature for a first order Signature for a first order

phase transition ?phase transition ?

-2 -1 0 1 2

-0.2

-0.1

0.0

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-2 -1 0 1 2-0.2

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-2 -1 0 1 2

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-2 -1 0 1 2

-0.1

0.0

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0.2

Pb+Pb, 40 A GeVprotons

central

v 1

Pb+Pb, 40 A GeVprotons

central

NA49 HSD UrQMD 3f-hydro

v 2

semi-central

v 1

NA49 HSD UrQMD 3f-hydrosemi-central

v 2

pT < 2 GeV/c peripheral

y

v 1

pT < 2 GeV/c

y

peripheral

v 2

4. 4. Collective flow: elliptic flow at 25 A GeV Collective flow: elliptic flow at 25 A GeV – predictions for CBM– predictions for CBM

0.0 0.5 1.0 1.5 2.0

0.00

0.05

0.10

0.15

0.20

v 2

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

AMPT w/o string melting AMPT with string melting QGSM (Dubna) QGSM (Oslo-Tuebingen) UrQMD HSD GiBUU

pT [GeV/c]

Charged particles

Transport models Transport models

• HSD HSD

• UrQMD UrQMD

• GiBUUGiBUU

• QGSM (v. Dubna;QGSM (v. Dubna; v. Oslo-Tuebingen)v. Oslo-Tuebingen)

•AMPT without string meltingAMPT without string melting

predict similar vpredict similar v22 for charged for charged particles!particles!

AMPT with string melting showsAMPT with string melting showsmuch stronger vmuch stronger v2 2 for charges for charges particlesparticles !!

4. 4. Collective flow: elliptic flow at 25 A GeV Collective flow: elliptic flow at 25 A GeV – predictions for CBM– predictions for CBM

0.0 0.5 1.0 1.5 2.0-0.10

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

p

K

D-Dbar HSD

pT [GeV/c]

p

K

QGSM: v. Dubna Oslo-Tuebingen

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

p

Kv 2

p

K

UrQMD

pT [GeV/c]

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

GiBUU

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

p

K

v 2

AMPT with string melting shows vAMPT with string melting shows v2 2 similar for all particlessimilar for all particles !!

5. 5. DileptonsDileptons

Dileptons are an Dileptons are an ideal probeideal probe for vector meson spectroscopy in for vector meson spectroscopy in the the nuclear mediumnuclear medium and for the nuclear dynamics ! and for the nuclear dynamics !

•Study of Study of in-medium effectsin-medium effects with dilepton experiments: with dilepton experiments:„„Historical“ overview – DLS, SPS (CERES, HELIOS)Historical“ overview – DLS, SPS (CERES, HELIOS) Novel experiments – HADES, NA50, CERES, PHENIXNovel experiments – HADES, NA50, CERES, PHENIX Future – Future – CBMCBM

• Excitation function for dilepton yieldsExcitation function for dilepton yields• Predictions for CBM (e+e- and Predictions for CBM (e+e- and ++-)-)

• Direct photons as a possible observable for CBM ?!Direct photons as a possible observable for CBM ?!

5. 5. Dileptons Dileptons

High precision NA60 data allow to distinguish among in-High precision NA60 data allow to distinguish among in-medium models!medium models!Clear evidence for a broadening of the Clear evidence for a broadening of the spectral spectral function!function!

5. 5. DileptonsDileptons

• Dilepton yield increases with energy due to a higher production of mesons Dilepton yield increases with energy due to a higher production of mesons • melts at practically all energies; melts at practically all energies; and and show clear peaks on an approx. show clear peaks on an approx. exponential background in mass!exponential background in mass!

0.2 0.4 0.6 0.8 1.0 1.2

10-5

10-4

10-3

10-2

10-1

100

0.2 0.4 0.6 0.8 1.0 1.2

10-5

10-4

10-3

10-2

10-1

100

50

20

21.5 A TeV160

105

3

2 A GeV

M [GeV/c 2]

dne+ e- /

dM [

(GeV

/c 2)

-1]

Au+Au, b=2 fm

HSD' 2000

in-medium meson spectral functionsfree meson spectral functions

5020

21.5 A TeV160

10

5

3

2 A GeV

M [GeV/c 2]

Au+Au, b=2 fm

5. 5. Dileptons – prediction for CBMDileptons – prediction for CBM

In-medium modifications of e+e- and In-medium modifications of e+e- and ++- spectra are very similar!- spectra are very similar!

0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

Au+Au, 25 A GeV, 5% centralee:

free in-medium

M [GeV/c2]

: free in-medium

dN/d

M [

1/(G

eV/c

2 )]

e+e

Au+Au, 25 A GeV, 5% central

M [GeV/c2]

rati

o=in

med

ium

/fre

e

0.0 0.2 0.4 0.6 0.8 1.0 1.2

10-4

10-3

10-2

10-1

100

101

102

0.0 0.2 0.4 0.6 0.8 1.0 1.210-4

10-3

10-2

10-1

100

free in-medium

M [GeV/c2]

Au+Au->e+e-+X 25 A GeV, 5% central

dN/d

M [

1/(G

eV/c

2 )]

HSD

free in-medium

M [GeV/c2]

Au+Au->+-+X 25 A GeV, 5% central

dN/d

M [

1/(G

eV/c

2 )]

6. 6. Open and hidden charmOpen and hidden charm

0 20 40 60 80 1000

10

20

30

40

50

0 20 40 60 80 100 120 1400

10

20

30

40

50

NA38 HSD

B(

J/)

/(D

Y)| 2.

9-4.

5

S+U, 200 A GeV

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

HSD UrQMD

B(

J/)

/(D

Y)| 2.

9-4.

5

Pb+Pb, 160 A GeV

ET [GeV]

Hidden charm: J/Hidden charm: J/ , , ‘ ‘

Anomalous J/Anomalous J/ suppression in A+A suppression in A+A (NA38/NA50)(NA38/NA50)

Comover dissociationComover dissociation in the in the transporttransport

approaches – approaches – HSD HSD && UrQMD UrQMD

NA50 data are consistent withNA50 data are consistent with

comover absorption models comover absorption models

Heavy flavor sectorHeavy flavor sector reflects the actual dynamics reflects the actual dynamics since heavy hadrons can since heavy hadrons can onlyonly be formed in the very be formed in the very early phaseearly phase of heavy-ion collisions at FAIR/SPS! of heavy-ion collisions at FAIR/SPS!

6. 6. Open and hidden charmOpen and hidden charm

New NA60 data for In+In at 160 A GeV: New NA60 data for In+In at 160 A GeV: no consistent description has no consistent description has been found so far with Glauber type comover absorption modelsbeen found so far with Glauber type comover absorption modelsNote:Note: no final transport calculations yet for In+In! no final transport calculations yet for In+In! (work in progress!)(work in progress!)

Satz, Digal, Fortuna to (percolation)Satz, Digal, Fortuna to (percolation)Rapp, Grandchamp, Brown (diss. and recomb.)Rapp, Grandchamp, Brown (diss. and recomb.)Capella, Ferreiro (comovers)Capella, Ferreiro (comovers)

6. 6. Open and hidden charmOpen and hidden charm

0 1 2 3 41300

1400

1500

1600

1700

1800

QCD sum rule

Coupledchannel

Ch. SU(4) model: MFT RHA

D

D

mD

[M

eV]

B/0

0 1 2 3 41300

1400

1500

1600

1700

1800

1900

QCD sum rule

Ch. SU(4) model: MFT RHA

mD

+ [M

eV]

2.0 2.5 3.0 3.510

-8

10-6

10-4

10-2

__

D+D

bare in-medium(2

mT)-1

dN/d

mT [G

eV-2

]

Au+Au, 25 A GeV, central

mT [GeV]

• Dropping D-meson massesDropping D-meson masses with increasing light quark density with increasing light quark density

might give a might give a large enhancement of the open charm yieldlarge enhancement of the open charm yield at 25 A GeV ! at 25 A GeV !

Open charm: D-mesonsOpen charm: D-mesons

HSDHSD

6. 6. Open and hidden charmOpen and hidden charm

In-medium reduction of D/Dbar In-medium reduction of D/Dbar massesmasses might have a might have a strong strong influence on influence on ‘ suppression‘ suppression due to due to the opening of the the opening of the ‘->D Dbar ‘->D Dbar decay channel [Rapp, Brown et al.]decay channel [Rapp, Brown et al.]

0 20 40 60 80 1000.000

0.005

0.010

0.015

0.020

HSD, set 1 HSD, set 2

co-mover model suppression in QGP

B

(')

'/B

(J/

)J/

S+U, 200 A GeV

0 20 40 60 80 100 120 140 1600.000

0.005

0.010

0.015

0.020

HSD, set 1 HSD, set 2

co-mover model suppression in QGP SCM

B

(')

'/B

(J/

)J/

Pb+Pb, 160 A GeV

ET [GeV]

The The ‘/J/‘/J/ ratio ratio gives information about the approach to chemical gives information about the approach to chemical equilibration: equilibration: charm chemical equilibrationcharm chemical equilibration is not achieved in HSD is not achieved in HSD since the since the ‘ mesons are more suppressed relative to J/‘ mesons are more suppressed relative to J/

0 1 2 3 410

-9

10-7

10-5

10-3

10-1

101

103

105

HSD

K

__

D+D: bare, in-med.J/ (2

mT)-1

dN/d

mT [

GeV

-2]

Au+Au, 25 A GeV, central

mT [GeV]

6. 6. Open and hidden charm -Open and hidden charm -predictions for CBMpredictions for CBM

Open charm: Open charm: without medium effectswithout medium effects: suppression of D-meson spectra by factor ~ 10 : suppression of D-meson spectra by factor ~ 10 relative to the global mrelative to the global mTT-scaling -scaling with medium effects:with medium effects: restoration of the global mrestoration of the global mTT-scaling for the mesons-scaling for the mesonsHidden charm: Hidden charm: J/J/suppression due to comover absorption at FAIR is lower as at SPSsuppression due to comover absorption at FAIR is lower as at SPS

20 40 60 80 100 120 140 1600.0

0.2

0.4

0.6

0.8

1.0

HSD

SJ/ s

urvi

val f

acto

r Au+Au (central)

Energy [A GeV]

Open charmOpen charmHidden charmHidden charm

CBMCBM

7. 7. Fluctuations and correlationsFluctuations and correlations

Multiplicity fluctuations Multiplicity fluctuations of negatively, positively and all charged of negatively, positively and all charged particles as a function of the number of particles as a function of the number of projectile participantsprojectile participants N Npartpart

proj proj : :

N

NN

N

Var(N)22

=1 - Poissonian multiplicity =1 - Poissonian multiplicity distribution with no distribution with no dynamical correlationsdynamical correlations

HSD and UrQMD show strong multiplicity fluctuations in 4HSD and UrQMD show strong multiplicity fluctuations in 4 ‚full‘ acceptance, ‚full‘ acceptance, however, the however, the observed (by NA49) non-trivial system size dependence of observed (by NA49) non-trivial system size dependence of multiplicity fluctuationsmultiplicity fluctuations is not reproduced by HSD and UrQMD ! is not reproduced by HSD and UrQMD !

Fluctuation and correlation measurements Fluctuation and correlation measurements provide provide information oninformation on susceptibilities of matter: susceptibilities of matter: rapid rapid changes reflect the changes reflect the order of the phase transitionorder of the phase transition

7. 7. Fluctuations and correlationsFluctuations and correlations

Predictions:Predictions: Excitation function of the Excitation function of the correlation coefficient Ccorrelation coefficient CBSBS for for central Pb+Pb and minimum bias p+p collisions calculated within central Pb+Pb and minimum bias p+p collisions calculated within UrQMD:UrQMD:

2

(n)nn

2(n)

(n)nn

(n)(n)n

(n)

BS

SN1

SN1

SN1

BN1

SBN1

3C

BB(n)(n) , S , S(n)(n) – baryon number and – baryon number and strangeness in a given event (n)strangeness in a given event (n)

Energy dependence of Energy dependence of event-event-by-event fluctuationsby-event fluctuations of the ratiosof the ratios

(K(K+++K+K--)/()/(++++--) and (p+pbar)/() and (p+pbar)/(++

++--) within the UrQMD model:) within the UrQMD model:

• FAIRFAIR is anis an excellent facilityexcellent facility toto study the properties of sQGP study the properties of sQGP (strongly interacting ‚color liquid‘) (strongly interacting ‚color liquid‘) as well as hadronic matter as well as hadronic matter

Summary

• Transport theory Transport theory is theis the general basisgeneral basis for an for an understanding of nuclear understanding of nuclear dynamics on a microscopic leveldynamics on a microscopic level

How to model a phase transition How to model a phase transition from hadronic to partonic matter?from hadronic to partonic matter? UrQMD: U+U, 25 A GeVUrQMD: U+U, 25 A GeV