Transcript Blume

Particle Production at the SPS
and the QCD Phase Diagram
Christoph Blume
University of Frankfurt
26th Winter Workshop
on Nuclear Dynamics
Ocho Rios, Jamaica
January 2010
Christoph Blume
University of Frankfurt
Winter Workshop on
Nuclear Dynamics,
2010, Ochos Rios, Jamaica
Outline
How to probe different regions of the QCD phase diagram?
Variation of center-of-mass energy
Way of scanning different freeze-out parameters T and μB
Variation of system size
How do T and μB depend on system size
Core corona approach
Critical point search
Systematic study of multiplicity fluctuations
Other observables
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
1
QCD Phase Diagram
A. Andronic et al.,
arXiv: 0911.4806
L. McLarren and
R.D. Pisarski,
Nucl. Phys. A796,
83 (2007).
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
2
QCD Phase Diagram
Experimental Access
High energies (RHIC/LHC)
B small
System reaches QGP phase
Low energies (AGS)
B large
System stays in hadronic phase
In between (SPS/FAIR)
Variation of B by changing sNN
Possible to localize critical point?
Other control parameters
(e.g. system size)?
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
3
Energy Dependence
Net-Baryon Distributions
NA49 preliminary
Significant change of
shape at SPS energies
Peak  dip structure
Rapid change of
net-baryon density
at y = 0
 Strong variation of B
Central Pb+Pb/Au+Au
158A GeV
E802
BRAHMS
Phys. Rev. Lett. 82
(1999), 2471
Phys. Rev. C 60
(1999), 064901
Phys. Rev. Lett. 93
(2004), 102301
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Energy Dependence
Example: /π- and /π-Ratios
NA49 data
Phys. Rev. C78,
034918 (2008)
/
|y| < 0.4
Statistical models
Generally good
description at all
energies
Fixes parameters
T and μB
−
/
-/
−+/

|y| < 0.5
 = 1.5 (+ + -)
SHM(B): A. Andronic et al.
Nucl. Phys. A 772, 167 (2006).
UrQMD: M. Bleicher et al.,
J. Phys. G 25, 1856 (1999)
and private communication
HSD:
E. Bratkovskaya et al.,
Phys. Rev. C69, 054907 (2004)
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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QCD Phase Diagram
Data Points
F. Becattini et al.,
Phys Rev. C69,
024905 (2004).
Results from different
beam energies
Analysis of particle yields
with statistical models
Freeze-out points reach QGP
phase boundary at top SPS
energies
Caveat: Disagreement between
different LQCD results on TC
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
6
System Size Dependence
Freeze-out Parameter
How do freeze-out
parameters depend
on system size ?
Statistical model fits
result in different T
Central reactions
Way to move around
in phase diagram?
F. Becattini et al.,
Phys. Rev. C73, 044905 (2005)
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
7
System Size Dependence
(Anti-)Proton y-Spectra
NA49
preliminary
p
p
Preliminary data by NA49
Minimum bias Pb+Pb at 158A GeV
Christoph Blume
NA49
preliminary
WWND 2010, Ocho Rios, Jamaica
H. Ströbele et al.
arXiv:0908.2777
8
System Size Dependence
Net-Protons
No strong system size
dependence observed
NA49 preliminary
p-p
Cen.
per.
Peripheral spectrum slightly
more pronounced y-dependence
than central one
p+p
Beam rapidity not measured!
central
In measured rapdity range
similar shape like p+p data
Per.
NA49 preliminary
⇒ System size has no
big influence on μB
p+p Data:
M. Aguilar-Benitz et al.,
Z. Phys. C 50 (1991), 405.
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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System Size Dependence
Enhancement factors of , , and 
Enhancement factor
p+p data: NA49
 1 dn Pb  Pb  

E 
 Nw

dy
y 0 

 1 dn p  p  


2

dy
y 0 

Early saturation
Nw > 60
Pb+Pb
Core Corona Model
f (NW ) = fraction of nucleons
that scatter more than once
C+C
M NW   NW  f NW  MCore
158A GeV
 1 f NW MCorona

Si+Si

F. Becattini and J. Manninen, J. Phys. G35, 104013 (2008)
K. Werner, Phys. Rev. Lett. 98, 152301 (2007)
J. Aichelin and K. Werner, arXiv:0810.4465
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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System Size Dependence
Average Transverse Mass: mt-m0
Similar dependence as
for multiplicities observed
|y| < 0.4 (0.5)
Early saturation Nw > 60
Core Corona model
f(NW ) = fraction of nucleons, that
scatter more than once

mt N W   N W f N W  mt
Core
 1  f N W  mt
Corona

F. Becattini and J. Manninen, J. Phys. G35, 104013 (2008)
K. Werner, Phys. Rev. Lett. 98, 152301 (2007)
J. Aichelin and K. Werner, arXiv:0810.4465
NA49 data:
Phys. Rev. C80 (2009), 034906.
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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System Size Dependence
Core-Corona: Central ↔ Peripheral
Core Corona model
f(Npart) = fraction of nucleons,
that scatter more than once
Centrality dependence
Stronger for smaller systems
Central reactions
Still clear change of fmax
with system size
Compare fmax(Pb+Pb) ≈ 0.9
and
fmax(C+C) ≈ 0.65
⇒ apparent change of T + μB
Not real, just different
mixture of core and corona
Thanks to K. Reygers for
providing the Glauber code
Christoph Blume
System size is not a
good control parameter
to move around in
QCD phase diagram
WWND 2010, Ocho Rios, Jamaica
12
System Size Dependence
Core-Corona: Asymmetric Systems
Core Corona model
f(Npart) = fraction of nucleons,
that scatter more than once
Centrality dependence
Peculiar shape for small
projectiles (e.g. C, O, Si, S)
Limiting case: p + A
f(Npart) = 1 / Npart
Model applicable in p+A?
First attempt in T. Šuša et al.,
Nucl. Phys. A698 (2002) 491c
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Theoretical Predictions
Lattice QCD difficult for B > 0
Sign problem in Fermion-determinant
Progress in recent years
(e.g. Fodor and Katz)
Results strongly divergent
Typically B > 200 MeV
Perhaps no critical point at all
for B < 500 MeV
(de Forcrand and Philipsen)
Christoph Blume
M. Stephanov,
CPOD conference 09
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Observables
Elliptic flow v2
R. A. Lacey et al., arXiv:0708.3512: η/s versus T and μB.
E. Shuryak, arXiv:hep-ph/0504048: Decrease (increase) of baryon (meson) flow.
Higher experimental precision required.
mt-Spectra of baryons and anti-baryons
Asakawa et al., Phys. Rev. Lett. 101 (2008) 122302.
Higher experimental precision required.
Di-pion (sigma) intermittency study
T. Anticic et al., arXiv 0912.4198.
No unambiguous signal seen yet
Fluctuations: multiplicity and/or 〈pt〉
Stephanov, Rajagopal, Shuryak, Phys. Rev. D60 (1999), 114028.
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Multiplicity Fluctuations
Charged multiplicity n
Extensive quantity
 tight centrality selection (1%)
to reduce volume fluctuations
Pb+Pb,
158A GeV
1 < y < ybeam
Scaled variance 
Energy dependence of 
Data narrower than Poisson ( < 1)
Trend reproduced by UrQMD
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Multiplicity Fluctuations
n-Fluctuations as a function of B
B from stat.
Phys. Rev. C79, model fit:
Position of
crit. point:
Amplitude of
Fluctuations:
Width of
crit. region:
044904 (2009)
Z. Fodor and S. Katz
JHEP 0404, 050 (2004)
M. Stephanov et al.
Phys. Rev. D60,
114028 (1999)
Y. Hatta and T. Ikeda,
Phys. Rev. D67,
014028 (2003)
NA49 data:
Christoph Blume
F. Becattini et al.,
Phys. Rev. C73,
044905 (2006)
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Elliptic Flow v2
Energy dependence
of v2 of protons and
pions
Large systematic effects
Especially for proton v2!
Clearly needs
improvements on
the experimental side
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Theoretical Predictions
Critical region
Larger area in T - B plane
Y. Hatta and T. Ikeda,
Phys. Rev. D67,
014028 (2003)
Focusing effect
Proximity of critical point
might influence isentropic
trajectories (nB/s = const.)
Askawa et al.,
Phys. Rev. Lett. 101,
122302 (2008)
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
mt-Spectra of Baryons and Antibaryons
Expectation: B/B ratio
should fall with mt
Askawa et al.,
PRL. 101, 122302 (2008)
No significant energy
dependence of slope a
observed
K. Grebieszkov et al.,
Nucl. Phys. A830 (2009), 547c
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Summary
How to probe different regions of the QCD phase diagram ?
Variation of center-of-mass energy
Good control parameter to move around in phase diagram
Variation of system size
Changes only relative contribution of core and pp-like corona
(if core-corona ansatz holds)
Change in T only apparent, μB = const.
Search for critical point
First results from multiplicity fluctuations negative
Need for better observables
Multi-dimensional (scale and pt-dependent) fluctuation studies
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Backup
22
System Size Dependence
p+A Collisions
No clear evidence for
decrease with Npart
Significant decrease visible
only for anti-lambda
Data not fully consistent
NA57: F. Antinori et al.,
J. Phys. G32 (2006) 427
NA49: T. Šuša et al.,
Nucl. Phys. A698 (2002) 491c
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
Di-Pion (Sigma) Intermittency
π+π- Pairs above di-pion
threshold
Factorial moments F2(M)
M: Number of bins in transverse
momentum space
Subtract mixed event background
⇒ ΔF2(M)
Search for power law behavior
ΔF2(M) ∼ (M2) Φ2
Φ2 : critical exponent
Φ2 > 0 for Si+Si
Coulomb effects become
an issue for larger systems
p+p, C+C, Si+Si at 158A GeV
T. Anticic et al. arXiv 0912.4198
N.G. Antoniou, F.K. Diakonos,
and G. Mavromanolakis
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Critical Point
pt-Fluctuations
Measure of pt-fluctuations
Energy dependence of pt
No significant variation with sNN
for central collisions
Trend reproduced by UrQMD
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
25
Critical Point
pt-Fluctuations
pt-Fluctuations as a function of B
B from stat.
Phys. Rev. C79, model fit:
Position of
crit. point:
Amplitude of
fluctuations:
Width of
crit. region:
044904 (2009)
Z. Fodor and S. Katz
JHEP 0404, 050 (2004)
M. Stephanov et al.
Phys. Rev. D60,
114028 (1999)
Y. Hatta and T. Ikeda,
Phys. Rev. D67,
014028 (2003)
NA49 data:
Christoph Blume
F. Becattini et al.,
Phys. Rev. C73,
044905 (2006)
WWND 2010, Ocho Rios, Jamaica
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Critical Point
System Size Dependence of n-Fluctuations
Stronger n-Fluctuations seen
in smaller systems
F. Becattini et al.,
Phys. Rev. C73,
044905 (2006)
Hypothetic critical point (CP2)
at T = 178 MeV and B = 250 MeV
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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System Size Dependence
dN/dy at Mid-rapidity for Λ, Ξ, and Ω
Transport models
OK for 
−
Slightly below 
Too low for 
UrQMD: H. Petersen et al.
arXiv: 0903.0396
HSD: W. Cassing and
E. Bratkovskaya,
Phys. Rep. 308, 65 (1999)
and private communication
Core Corona model
OK for  and 
F. Becattini and J. Manninen,
Phys. Lett. B673, 19 (2009)
J. Aichelin and K. Werner,
arXiv:0810.4465
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
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Energy Dependence
Total Multiplicities
AGS NA49
Central A+A collisions
RHIC
Only total multiplicities (4) shown
Chemical freeze-out
Experimental points in T-B plane
Analysis with statistical models
Baryons (stopping)  B
Strange particles
 T (+ B)
Phase boundary reached ?
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
29
QCD Phase Diagram
Phase Boundary for B = 0
Lattice QCD
General consensus:
cross over for B = 0
Critical Temperature Tc
Depends on order parameter
e.g. chiral condensate:
l ,s    
or s-quark susceptibility s
2mu ,d
ms
ss
Significant differences between collaborations
(Budapest-Wuppertal, Riken-Bielefeld-Columbia “hotQCD”)
Figs. and table: Budapest-Wuppertal-Group,
Y. Aoki et al., arXiv:0903.4155.
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
30
QCD Phase Diagram
K. Rajagopal, MIT
CPOD conference 09
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
31
Strangeness in Heavy Ion Reactions
Statistical Models
Assumption:
Multiplicities are determined by
statistical weights (chemical equilibrium)
Grand-canonical partition function:
A. Andronic,
P. Braun-Munzinger,
and J. Stachel,
arXiv: 0812.1186
Parameters:
V, T, B, (s)
Allows in general excellent fits
to measured multiplicities
F. Becattini et al.,
Phys. Rev. C69,
024905 (2004)
Limits of applicability ?
 Rare particles and low energies
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
32
Energy Dependence
K+/π+ and /π--Ratios
Extended statistical model
Higher mass resonances included
(up to 3 GeV)
 Improved description of
pions and thus of the K+/+-ratio
Limiting temperature reached
in SPS energy region
Equilibration due to
proximity of phase
boundary?
A. Andronic, P. Braun-Munzinger
and J. Stachel, arXiv:0812.1186.
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
33
Energy Dependence
K+/π+-Ratio: Comparison to STAR Data
STAR measurements
at lower energies
√sNN = 9.2 + 19.6 GeV
STAR: L. Kumar et al.,
SQM2008
arXiv:0812.4099
Good agreement
with NA49 data
Christoph Blume
WWND 2010, Ocho Rios, Jamaica
34