1. Phase transitions and critical fluctuations
Scale-dependent analysis of
<pt> correlations
Harald Appelshäuser
Institut für Kernphysik
Goethe Universität Frankfurt
CERES, Nuclear Physics A811 (2008)
Phd thesis Georgios Tsiledakis
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

2. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
QCD phase diagram T
QGP
Hadrons μB
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

3. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
QCD phase diagram
from Forcrand and Philipsen, JHEP 01 (2007)
The more is understood, the less is known.
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

4. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
QCD phase diagram
Andronic, Braun-Munzinger, Stachel NPA772 (2006)
at all energies, all hadron
abundancies are in thermal
equilibrium  T, μB
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

5. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
QCD phase diagram
Andronic, Braun-Munzinger, Stachel; arXiv:
a temperature limit (≈165 MeV) is
reached beyond √sNN≈10 GeV
Hagedorn‘s limiting temperature?
higher temperatures must „exist“ though,
but not in the hadronic world!
 The phase transition?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

6. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
fluctuations
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

7. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
fluctuations
Temperature fluctuations are suppressed
in the vicinity of the phase boundary
if <pt> is measure for T, <pt> fluctuations should
also be suppressed
Stodolsky, PRL 75 (1995)
Shuryak, PLB423 (1998)
Stephanov, Rajagopal, Shuryak PRL 81 (1998)
BUT: <pt> may not be a good measure for the temperature:
Stephanov, Rajagopal, Shuryak PRD 60 (1999):
BE-occupation number fluctuations,
effects of thermal contact of pions to heat bath,
coupling of pions to fluctuating sigma field etc etc etc
 <pt>fluctuations should be enhanced, in particular in the vicinity of the CP
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

8. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
fluctuations
LQCD Allton et al., PRD 71 (2005)
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

9. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
QCD phase diagram
expect divergence of susceptibilities
near the critical point
detectable by correlation/fluctuation
measurements (e.g. mean pt)
locate the critical point in the T-mb plane
by variation of an experimental control
parameter x (√s, centrality,…) T
quarks and gluons
deconfined
~170
MeV
critical point
hadrons
confined
color
superconductor x σ2 m0 mb
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

10. search for fluctuations?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

11. search for pt-fluctuations
LQCD:
ideal world
Heavy-ion collision:
finite system size and lifetime, thermalization?
can signatures survive subsequent evolution?
other sources of „fluctuations“ (correlations):
E- and p-conservation
resonance decays
collective flow
quantum statistics
mini-jets and their modification
etc
detector effects
need a model
which describes
all this correctly
this model
doesnt exist
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

12. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
pt fluctuations in AA
STAR PRC72 (2005)
central Pb-Au
Au-Au
CERES NPA727(2003)97
s2pt,dyn = s2data - s2mixed
dynamic contribution is quadratically small
but significant
Mpt (GeV/c)
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

13. Energy dependence in AAx σ2
CERES, NPA811 (2008)
dynamic contribution is independent of beam energy  trivial?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

14. Energy dependence in AA
Braune et al. Phys.Lett. 123B (1983)
~12%
CERES, NPA811 (2008)
dynamic contribution is independent of beam energy  trivial?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

15. Energy dependence in AA
Braune et al. Phys.Lett. 123B (1983)
UA5 Phys.Rep. 154 (1987)
~12%
CERES, NPA811 (2008)
dynamic contribution is independent of beam energy  trivial?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

16. pt fluctuations – centrality dependence
NA49
NA49 PRC70 (2004)
CERES, JPG30(2004)
CERES
strong decrease of correlations
in more central events
 dilution
non-trivial centrality
dependence
 thermalization, flow
saturation, elliptic flow,
jets, phase transition,
percolation point,
critical point…?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

17. scale-dependent analysis
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

18. scale-dependent analysis
the scale dependence of momentum correlations carries information
about their origin and may allow a separation of different contributions
are correlations short- or long-ranged in φ, η, pt?
momentum correlator <Δpt,iΔpt,j> :
STAR PRC72(2005)
in inclusive analyses:
but correlator allows also a selection in Δη, Δφ, Δpt, charge,…
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

19. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
CERES Experiment
0 < f < 2p
2.1 < h < 2.6
TPC
2000: 158 AGeV/c 35M Pb-Au events
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

20. scale-dependent analysis - ΔφΔη
central Pb-Au 158 AGeV
<Δpt,iΔpt,j> (MeV/c)2
CERES, NPA811 (2008)
dominant short-range component
weak back-to-back structure
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

21. scale-dependent analysis - ΔφΔη
central Pb-Au 158 AGeV
<Δpt,iΔpt,j> (MeV/c)2
<Δpt,iΔpt,j> (MeV/c)2
<Δpt,iΔpt,j> (MeV/c)2
CERES, NPA811 (2008)
short range component from quantum correlations (HBT)
very short range component from Coulomb, e+e-
weak bump from resonances
back-to-back component
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

22. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
pt-pt correlations
cumulant pt variable x(pt):
x(pt)
CERES, NPA811 (2008)
pt (GeV/c)
pt (GeV/c)
 x1(pt) vs. x2(pt) is flat in the absence of correlations
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

23. pt-pt correlations – Δφ dependence
CERES, NPA811 (2008)
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

24. pt-pt correlations – charge dependence-- ++ +-
0 < Δφ < 300
CERES, NPA811 (2008)
150 < Δφ < 1800
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

25. scale-dependent analysis – centrality dependence
CERES, NPA811 (2008)
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

26. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
CERES, NPA811 (2008)
<Δpt,iΔpt,j> (MeV/c)2
158 AGeV Pb-Au central
CERES
preliminary Δφ
shape and magnitude of flow dont match the data
reminiscent of high-pt triggered correlations
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

27. scale-dependent analysis – centrality dependence
CERES, NPA811 (2008)
centrality dependence is strongly Δφ-dependent
around 60 degrees fluctuations are very small
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

28. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009
summary
pt fluctuations exhibit a strong scale dependence
observed structures can be qualitatively assigned to „trivial“ correlations
from HBT, Coulomb, flow, minijets (not yet quantitatively confirmed)
small margin for „critical“ fluctuations, if any
is this consistent with initial state fluctuations, and thermodynamics,
i.e finite CV ?
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009

29. Harald Appelshäuser, EMMI workshop Münster, Feb. 18-20, 2009x σ2 ? x σ2
Harald Appelshäuser, EMMI workshop Münster, Feb , 2009