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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
0.10
0.15
0.20
0.25
100 101 102 103 1040.00
0.05
0.10
0.15
0.20
0.25
100 101 102 103 104
0.00
0.05
0.10
0.15
0.20
0.25
100 101 102 103 104
0.00
0.05
0.10
0.15
0.20
0.25
100 101 102 103 1040.00
0.02
0.04
0.06
0.08
100 101 102 103 1040.00
0.02
0.04
0.06
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
0.20
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
0.1
0.2
-2 -1 0 1 2-0.2
-0.1
0.0
0.1
0.2
-2 -1 0 1 2
-0.2
-0.1
0.0
0.1
0.2
-2 -1 0 1 2
-0.1
0.0
0.1
-2 -1 0 1 2
-0.2
-0.1
0.0
0.1
0.2
-2 -1 0 1 2
-0.1
0.0
0.1
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
-0.05
0.00
0.05
0.10
0.15
0.0 0.5 1.0 1.5 2.0-0.10
-0.05
0.00
0.05
0.10
0.15
0.0 0.5 1.0 1.5 2.0-0.10
-0.05
0.00
0.05
0.10
0.15
0.0 0.5 1.0 1.5 2.0-0.10
-0.05
0.00
0.05
0.10
0.15
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