Transcript Energy Dependence of Hadronic Observables

Review of Structures in the Energy
Dependence of Hadronic Observables
Christoph Blume
Int. Workshop on
Critical Point and
Onset of Deconfinement
Florence, July 3-6, 2006
Introduction
Exploring the QCD Phase Diagram
Chemical freeze-out
points approach phase
boundary at SPS energies
Critical point
1st order
Cross over
Transition to QGP likely
to happen in this region
Ebeam = 20 - 158 AGeV
(sNN = 6.3 - 17.3 GeV)
Lattice calculations:
Fodor and Katz
Bielefeld-Swansea group
Hadron gas fits ():
J. Manninen et al.
Christoph Blume
Florence, July 3-6 2006
2
Introduction
Energy Dependence
Any evidence for a phase transition (or the even critical point)
in hadronic observables seen ?
Look for “non-smooth” behaviour in the energy dependencies
Prominent examples: “horn”, “kink”, “step”
Any other structures?
How significant are they?
Comparison to hadronic models
Transport models (UrQMD + HSD)
Statistical models
Identify “trivial” structures
Baseline comparison
Christoph Blume
Florence, July 3-6 2006
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Introduction
Hadronic Scenery at SPS
Transition from baryon
dominated to meson
dominated system
Statistical model:
Transition at sNN  8 GeV
Maximum of strangeness prod.
Evidences for structures
beyond this?
Christoph Blume
J. Cleymans, H. Oeschler, K. Redlich,
and S. Wheaton, hep-ph/0510283
Florence, July 3-6 2006
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Introduction
/Nw
K++
”Horn” / “Kink” / “Step”
HORN
Christoph Blume
KINK
Florence, July 3-6 2006
STEP
5
Introduction
Experiments
SPS
AGS
RHIC
Experiments
Ebeam (A GeV)
snn (GeV)
System
Particles
AGS
E802, E866, E877,
E891, E895, E917
2-10.7
2.7-4.9
Au+Au
, K, p, 
SPS
NA45, NA49, NA57,
(NA44, WA98)
20-158
6.3-17.3
Pb+Pb
, K, p, , ,
, ,...
RHIC
STAR, PHENIX,
BRAHMS, PHOBOS
-
20.0-200.0
Au+Au
, K, p, , ,
, , ...
Christoph Blume
Florence, July 3-6 2006
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Introduction
Observables
Particle yields
Pions
Strangeness
Transverse mass spectra
Radial flow  EOS
Elliptic flow
Initial pressure
Bose-Einstein correlations
System size and lifetime
Not discussed here: Fluctuations
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Energy Dependence of Particle Ratios
UrQMD + HSD
E.L. Bratkovskaya et al.,
PRC 69 (2004), 054907
Statistical hadron gas:
P. Braun-Munzinger,
J. Cleymans, H. Oeschler,
and K. Redlich
Nucl. Phys. A697
(2002) 902

  1.5     

K+/+
-/
s = 1
Full chem.
equilibrium
baseline
K-/-
/
Christoph Blume
/
Florence, July 3-6 2006
-++/
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Particle Yields
s = 1
(data – model)/(data)
Statistical hadron gas:
P. Braun-Munzinger,
J. Cleymans, H. Oeschler,
and K. Redlich
Nucl. Phys. A697
(2002) 902
(data – model)/(data)
Comparison to Statistical Model
?
Kaons and 
deviate from
stat. model for
sNN  7-8GeV
?
Different situation
for hyperons
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Position of Maxima
Statistical model
prediction:
Ratio
Maximum at
sNN (GeV)
K+/+
10.8
/
5.1
-/+
10.2
-/+
27.0
J. Cleymans, H. Oeschler, K. Redlich,
and S. Wheaton, hep-ph/0510283
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Local Slope of Energy Dependence:  and K
N i 1  N i 
N 

 sN N
s N N i 1  s N N i 


No significant structure for pions
Indications for sudden changes in kaon e.-dependence (?)
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Comparison s- and s-Carriers
s-quark carriers:
K-, K0
 (incl. 0)
0,-, ±
(1)
K+ , K0
 (incl. 0)
0,+, +
±
(1)
Data: E802, E866, E895, E917, NA49
 1.5 (+ + -)
(2)
(3)
s-quark carriers:
(2)
(3)
(1) K0  K+, K0  K- by isospin symmetry
(2) Taken from hadron gas fit by
 1.5 (+ + -)
Becattini et al., if not measured.
(3) Empirical factor
assumed.
(
+ ) /  = 1.6
Sudden change of strangeness production at sNN = 7-8GeV ?
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Local Slope of Energy Dep.: s/s-Quarks
Local slope seems
to change quite fast
for strangeness at
sNN = 7-8GeV
Smoother dependence
for pions
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
(Anti-)Strangeness to Pion Ratio
Maximum in
strangeness/pion
ratio
Same for s
and s quarks
Difficult to model in hadronic scenarios
Solid line: Statistical hadron gas model with s = 1
K. Redlich, priv. comm.
Predicted as signal for the onset of deconfinement
Dotted line: M. Gazdzicki and M.I. Gorenstein, Acta Phys. Polon. B30 (1999), 2705
Christoph Blume
Florence, July 3-6 2006
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Transverse Mass Spectra
Energy Dependence of mt-m0

negatively charged
Energy dependence of transverse activity seems to
change around sNN = 7-8GeV
General feature for pion, kaons and protons
Quite robust observation
Christoph Blume
Florence, July 3-6 2006
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Transverse Mass Spectra
Local Slope of Energy Dependence: mt-m0
Significant change of local slope for
pions and kaons around sNN = 7 GeV
 mt


 sN N

mt
i 1
 mt
i 
s N N i 1  s N N i 
Similar for protons
Christoph Blume
Florence, July 3-6 2006
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Elliptic Flow
Energy Dependence of v2 for Pions
Mid-rapidity data,
pt integrated
Initial spatial anisotropy
 different pressure gradients
 momentum anisotropy v2
Christoph Blume
Energy dependence
changes in SPS region
Florence, July 3-6 2006
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Elliptic Flow
Model Comparison of v2 for Pions
Energy dependence of v2
not described by UrQMD
Squeeze-out at lower
energies not described
w/o nuclear potential
At higher energies:
lack of inital pressure!
Indication for onset of
partonic flow at SPS?
Christoph Blume
H. Petersen, Hot Quarks06
Florence, July 3-6 2006
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Elliptic Flow
v2 for Protons at 40A GeV
Disappearance of proton flow?
Evidence for 1st order phase transition
H. Stöcker, nucl-th/0406018
?
Standard method different to
cumulant method at mid-rapidity
Larger systematic error
Systematic study with higher
precision needed
Challenge for future experiments!
NA49
PRC 68 (2003) 034903
Christoph Blume
Florence, July 3-6 2006
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Bose-Einstein Correlations
Energy Dependence of Radius Parameters
Christoph Blume
Florence, July 3-6 2006
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Bose-Einstein Correlations
Energy Dependence of Radius Parameters
No indication for strong
energy dependence
between AGS and RHIC
Structures?
But: Unresolved
discrepancies
between SPS
experiments!
Christoph Blume
kt  0.2GeV/c
Florence, July 3-6 2006
21
Bose-Einstein Correlations
Model Comparison: UrQMD
Eb
NA49 data
S
O
L
(20A GeV)
10
20A – 158A GeV
NA49 data:
8
;
th:
6
4
2
(30A GeV)
10
0
8
6
4
2
(40A GeV)
8
6
4
2
0
(80A GeV)
R i [fm]
0
8
6
4
2
Reasonable
description
by transport model
(160A GeV)
0
8
6
4
2
0
0
100
200
300
400
0
100
300
400
0
100
200
300
400
500
kT [MeV/c]
(R2out-R2side)1/2 slightly larger in model
Christoph Blume
200
Florence, July 3-6 2006
M. Bleicher, GRC06
QingFeng Li, Frankfurt
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Bose-Einstein Correlations
Model Comparison: UrQMD
Squares: kT=100 MeV/c
8
R s (fm)
No structure in energy
dependence in data and
transport model
10
Circles: kT=200 MeV/c
6
4
2
 Data
0
8
R o (fm)
6
exp (stars):
kT~150: E2,4,6,8,
4
2
E20,30,40,80,160 (NA49)
kT~170: s130
0
kT~200: E10.7,s62.4,s200
R L (fm)
8
M. Bleicher, GRC06
QingFeng Li, Frankfurt
E40,80,160 (CERES)
6
4
2
0
1
10
100
1000
10000
Eb (A GeV)
Christoph Blume
Florence, July 3-6 2006
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Summary
Evidences for structures in hadronic exciation functions
Around sNN = 7-8GeV
Particle Yields
Qualitatively close to to statistical model expectations
Clear deviations seen for kaons and 
Maxima in X/ ratios as in stat. model ?
Indication for sudden change in strangeness e.-dep.
Transverse mass spectra
Sudden change of mt
Change of radial flow  EOS ?
Elliptic flow
No clear evidence, higher presision data needed
Bose-Einstein correlations
No evidence for structure
High precision data mandatory!
Christoph Blume
Florence, July 3-6 2006
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Thanks!
Christoph Blume
Florence, July 3-6 2006
25
High pt
Energy Dependence of RCP for Pions and hStrongest drop of RCP
between s = 17.3GeV
and s = 62.4GeV
RpA
Any onset at low energies?
?
SPS
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Energy Dependence of K+/+
Central Pb+Pb/Au+Au
Mid-rapidity ratios
Same structure as for 4
Christoph Blume
Florence, July 3-6 2006
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Particle Yields
Energy Dependence of 4 Yields
AGS NA49
Central Au+Au, Pb+Pb
BRAHMS
Access to the energy
dependence of identified
particle yields in the
range sNN = 2.5 – 200 GeV
Christoph Blume
Florence, July 3-6 2006
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Transverse Mass Spectra
Inverse Slope Parameters of Kaons
Y. Hama et al.
Braz. J. Phys. 34 (2004), 322,
hep-ph/0309192
Feature cannot be described
by transport models
Hydro calculation with
assumption of 1st
order phase transition
 Change of EOS seen?
Christoph Blume
Florence, July 3-6 2006
29
Transverse Mass Spectra
Inverse Slope Parameters of Kaons
Step in energy dependence
Seems to be absent in p+p
p+p compilation from:
M. Kliemant, B. Lungwitz,
and M. Gazdzicki,
PRC 69 (2004) 044903
Christoph Blume
Florence, July 3-6 2006
30
Transverse Mass Spectra
“Hydro” - Model
Basic model:




Common freeze-out of all particle types
Boost invariant longitudinal expansion
Transverse expansion is modelled by a velocity profile
“Standard” version:
dN
 mt cosh    pt sinh  
mK
I
Schnedermann, Sollfrank, and Heinz,
Phys. Rev. C46
mt dmt dy
t
1


T
 0
 
T


  tanh1  t
Extended version:
 Resonance contribution included
U. Wiedemann and U. Heinz,
Phys. Rev. C56 (1997) 3265
B. Tomasik, nucl-th/0304079
 Baryonic resonances introduce dependence on B
 Chemical freeze-out: Tch and B taken from freeze-out curve
 Thermal freeze-out: System cools down, therefore assume:
 Conservation of entropy
 Conservation of effective particle numbers
Christoph Blume
Florence, July 3-6 2006
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Transverse Mass Spectra
“Hydro” – Model Fits
-
K-
p
Convave
Exponential
Shoulder
 Resonances
 Radial flow
E895: nucl-ex/0306033
NA49: Phys. Rev. C66 (2002) 054902, nucl-ex/0403023
PHENIX: Phys. Rev. C69 (2004) 024904, nucl-ex/0307022
Christoph Blume
Florence, July 3-6 2006
32
Transverse Mass Spectra
Energy Dependence of Fit Parameter
Fit to -, K- and p
Tch
Box-shaped
source profile
and linear
velocity profile
Fit range
0.1 < mt-m0 < 0.8 GeV
Energy dependence of Tf seems to change around 30 AGeV
Thermal and chemical freeze-out different? Single freeze-out model?
Continous increase of T
Christoph Blume
Florence, July 3-6 2006
33
Transverse Mass Spectra
Blast Wave Fits
Blast wave
implementation:
F. Retiere and
M. Lisa
nucl-th/0312024
Fit parameters:
T , R , 0 ,  , o
Good description of all particle species at SPS energies
Christoph Blume
Florence, July 3-6 2006
34
Bose-Einstein Correlations
Blast Wave Model Fits
Combined fit to HBT radii
and transverse mass spectra
Emission function:
1
 (   0 ) 2  

 22  exp(Ku / T)  1
S(x, K)  m t cosh(  Y)  ( R , s ) exp 
Fit parameters:
T , R , 0 ,  , o
Good fit to the data
slight deviations in Rside at high kt
Blast wave implementationn:
M. Lisa, F. Retiere, nucl-th/0312024
Christoph Blume
Florence, July 3-6 2006
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Bose-Einstein Correlations
Thermal Freeze-Out Parameters
Tchem
J. Cleymans, K. Redlich,
Phys. Rev. C60, 054908 (1999)
Slightly increasing temperature with beam energy
Approx. constant transverse geometrical Radii (Rbox 2Rgauss)
Finite emission duration at SPS energies
Christoph Blume
Florence, July 3-6 2006
36
Bose-Einstein Correlations
Energy Dependence of Freeze-Out Volume
Minimum in freeze-out
volume in SPS region
Possible explanation:
Constant mean free path
freeze-out condition
f 
V
1
 f
f   N  
Transition baryon 
meson dominated
N   N N  N  N   
But: Unresolved inconsistencies
between SPS experiments!
Christoph Blume
D. Adamová et al. (CERES collaboration),
Phys. Rev. Lett. 90 (2003) 022301.
Vf  2 
Florence, July 3-6 2006
3/ 2
2
 Rlong  Rside
37
Bose-Einstein Correlations
Energy Dependence of Freeze-Out Volume
kt  0.15GeV/c
Christoph Blume
Florence, July 3-6 2006
38
Particle Yields
Antilambda-Antiproton Ratio
Increase above 1 towards
lower energies
consistent with recent NA49 data
Models predict ratio < 1
Hadron Gas 1: J. Manninen et al.
Hadron Gas 2: K. Redlich et al.
Hadron Gas 3: J. Rafelski et al.
Christoph Blume
Florence, July 3-6 2006
39
Particle Yields
Antibaryon-Baryon Ratio
Strong increase of B/B ratio
in SPS energy range
Energy dependence weakens
with increasing strangeness
content
No indications for structures
in energy dependence
Christoph Blume
NA49 preliminary
Lines: Statistical hadron gas model
J. Manninen et al.
Fit to 4 data!
Florence, July 3-6 2006
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