1. Understanding the Properties of Chemical Freeze-Out
NICA/JINR-FAIR Workshop
“Matter at highest baryon densities
in the laboratory and in space”
April 2 – 4, 2012
FIAS
Christoph Blume
University of Frankfurt

2. Outline The QCD phase diagram Chemical freeze-out
Results from statistical model fits
Role of phase boundaries
Deconfinement phase transition (low μB)
Quarkyonic phase transition (high μB)
System size dependence
Freeze-out parameters vs. Npart
Indications for long lived hadronic phase ?
Current experimental situation
Early decoupling
Rare particles with low hadronic cross sections
Measurements at low energies
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

3. The QCD Phase Diagram Broad experimental program New exotic phases?
Past: SPS (and AGS)
Present: RHIC and SPS
Future: FAIR and NICA
What can be learned at low energies?
New exotic phases?
Quarkyonic matter
Can phase boundaries be mapped by hadron yields ?
RHIC
SPS
FAIR
NICA
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

4. The QCD Phase Diagram Experimental Access
Control parameter: √sNN
Allows to scan different regions of phase diagram
System freezes out at different positions along freeze-out curve
Trajectory might cross critical area
Variation of system size
Program of
H. Stöcker, E.L. Bratkovskaya,
M. Bleicher, S. Soff, and X. Zhu,
JPG31, S929 (2005)
Y.B. Ivanov, V.N. Russkikh,
V.D. Tonnev,
PRC73, (2006)
3-fluid hydro
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

5. Chemical Freeze-Out Statistical Model Fits
Assumption:
Multiplicities are determined by
statistical weights (chemical equilibrium)
Grand-canonical partition function:
Parameters:
V, T, B, (s)
Allows in general excellent fits
to measured multiplicities
Andronic et al.
Phys. Lett. B673, 142 (2009).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

6. Chemical Freeze-Out Energy Dependence
L. Kumar, QM11
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

7. Chemical Freeze-Out Where does Equilibration Happen?
Dynamical equilibration?
QGP phase at high energies
How about lower energies?
Hadron gas phase sufficient?
Other mechanisms?
Phase space dominance?
Hadronization always leads to statistical equilibrium?
Experiment
Any evidences for long lived hadron gas phase after?
Systematic studies at low energies
U. Heinz, Nucl. Phys. A661, 140 (1999).
R. Stock, Phys. Lett. B456, 277 (1999).
M. Gazdzicki and M. Gorenstein,
Acta Phys. Polon. B30, 2705 (1999).
J. Hormuzdiar et al.,
Int. J. Mod. Phys. E12, 649 (2003).
V. Koch, Nucl. Phys. A715, 108 (2003).
F. Becattini, arXiv:
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

8. Chemical Freeze-Out Continuous Freeze-Out
Dynamical decoupling
Should happen over certain time span
and temperature range
Theoretical approaches
Hydro + hadronic transport (e.g. UrQMD)
Hydro + extended freeze-out condition
System size dependence
Interplay mean free path and system size
⇒ decrease of T with increasing size (?)
Hadronic cross section
Rare particles (e.g. Ω) with low cross section ⇒ earlier freeze-out
H. Petersen et al.,
PRC78,
(2008)
Hydro-
phase
S. Bass and A. Dumitru, PRC61, (2000).
J. Knoll, NPA821, 235 (2009)
H. van Hecke, H. Sorge, N. Xu, PRL81, 5764 (1998).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

9. Chemical Freeze-Out Role of Phase Boundaries
Equilibration
Driven by proximity of freeze-out to phase boundary
Deconfinement transition at low μB
How about high μB?
Quarkyonic matter
Provides another phase boundary
Would determine position of chemical freeze-out points for higher μB
Consequence: no need for an extended hadronic phase
But: conjecture might be wrong ...
P. Braun-Munzinger, J. Stachel, and C. Wetterich,
PLB596, 61 (2004).
A. Andronic et al.,
Nucl. Phys. A837, 65 (2010).
L. McLarren and R.D. Pisarski,
Nucl. Phys. A796, 83 (2007).
S. Floerchinger and C. Wetterich
arXiv:
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

10. System Size Dependence Kinetic Freeze-Out
Tkin decreases with
increasing system size
Dynamical decoupling: interplay mean free path and size of system
Hydro reproduces trend
Freeze-out condition:
STAR: PRC83, (2011)
U. Heinz and G. Kestin, PoS(CPOD2006), 038
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

11. System Size Dependence Chemical Freeze-Out at small μB
Different behaviour
of Tkin and Tch
Tkin: clear centrality dependence
Tch: no centrality dependence
Difficult to reconcile with hydro for normal HG
Requires scattering rate
proportional to Tn with n ≥ 20
At phase boundary: τΩ ∝ T-60
STAR: PRC83, (2011)
U. Heinz and G. Kestin, PoS(CPOD2006), 038
P. Braun-Munzinger, J. Stachel, and C. Wetterich,
PLB596, 61 (2004).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

12. System Size Dependence Chemical Freeze-Out at higher μB (SPS)
Tch changes with system size
Central events of different A
μB independent on system size
Different freeze-out behaviour
at different energies ?
Careful systematic study needed
Geometric effects (“core-corona”)
might be important
F. Becattini et al.,
PRC73, (2005)
√sNN
Tch(p+p)
Tch(Au+Au/Pb+Pb)
17.3 GeV
181.5 MeV
157.5 MeV
200 GeV
170.1 MeV
168.5 MeV
F. Becattini et al., PRC73, (2006),
EPJC66, 377 (2010).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

13. System Size Dependence Geometrical Effects (“Core-Corona”)
Elementary N+N collisions
Core:
Dense fireball
System size dependencies determined by ratio core/corona
f (NW) = fraction of nucleons that scatter more than once (Glauber model)
P. Bozek, Acta Phys. Polon. B36, 3071 (2005).
F. Becattini and J. Manninen, J. Phys. G35, (2008)
J. Aichelin and K. Werner, Phys. Rev. C79, (2009)
K. Werner
158A GeV
C.B.
J.Phys.Conf.Ser.
230, (2010)
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

14. System Size Dependence Chemical Freeze-Out at higher μB (RHIC)
Recent STAR data
Beam Energy Scan program
Also significant system size dependence observed
BUT:
Tch increases with system size!
Opposite trend than observed by NA49
Contrary to naive expectation ?
⟶ Contribution by D. Blaschke
pp data?
L. Kumar,
CPOD11
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

15. Early Decoupling Rare Particles
Particles with low hadronic cross section
E.g. multi-strange baryons (Ω)
Might decouple earlier if there was a long lived hadronic phase
Deviations from statistical model fits?
No evidence seen
at RHIC and SPS
More precise data on multi-strange particles (low energies) will be helpful
Andronic et al.
Phys. Lett. B673, 142 (2009).
-/
 = 1.5 (+ + -)
NA49: PRL94,
(2005).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

16. Early Decoupling Strange Baryon to Pion Ratios
Λ/π _
Λ/π
X. Zhu, SQM11
Ξ-/π
Ξ+/π _
Good agreement between SPS and RHIC
Close to statistical model curve
Low energy data scarce ⟶ FAIR and NICA
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

17. Early Decoupling Statistical Model Fits at Low √sNN
M. Lorenz, CPOD11
HADES data:
Ar+KCl at √sNN = 2.61 GeV
Good agreement with
statistical model fit
Except: Ξ-!
Off by factor 25
Sub-threshold production
Also deviations for η (TAPS)
Freeze-out parameter fit into known systematics
How about system size dependence?
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

18. Early Decoupling Hydro + Cascade Predictions
No real effect for Ωs
No effect expected if Ω enters hadronic phase with equilibrium yield
Strong effect on antibaryons
Cascade removes p, Ξ+
⇒ Reduction from chemical equilibrium
Caveat: multi-meson fusion processes not included
First implementation in transport: HSD
(anti-protons)
S. Bass and A. Dumitru,
PRC61, (2000). _ _
R. Rapp and E. Shuyak, PRL86, 2980 (2001).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

19. Early Decoupling Antibaryons
Effect on statistical model fits
Fits with and w/o antibaryons
Studies ongoing
System size dependence of p
Tends to decrease towards central
Indication for absorption in hadronic
phase or just evolution of baryon number transfer ?
Right now inconclusive
High precision data required
R. Stock et al., arXiv:
NA49:
PRC83, (2011) _
STAR: PRC83, (2011)
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

20. Early Decoupling Antibaryons
Antibaryons removed by hadron gas phase ?
Simulation with hydro model + hadronic afterburner (UrQMD)
Afterburner removes antibaryons (p, Λ, Ξ) ⇒ Reduction from chemical equilibrium value
Caveat: multi-meson fusion processes not simulated
No final conclusion
from data yet
High precision data needed
H. Petersen et al., PRC78, (2008)
R. Stock et al.,
arXiv:
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

21. Early Decoupling Particle Ratios at LHC
p/π- and K-/π- ratios
p/π-(LHC) = K-/π-(BRAHMS+PHENIX)
(STAR: not feed down corrected!)
K-/π-(LHC) = K-/π-(RHIC) _
p/π- _ _
M. Floris, QM11
Statistical model predictions
Note: fit to larger set of particles
(π, K, p, Λ, Ξ, Ω) results in
expected Tch, problem only with p, p _
K-/π-
M. Floris, QM11
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

22. Conclusions Freeze-out properties at low energies
Indications for presence of phase boundary to quarkyonic matter?
⟶ drives particle yields to equilibrium
If yes, no need for extended hadron gas phase
Indicators:
No system size dependence of freeze-out parameter
No modification of rare particle yields (Ω, antiprotons)
Experimental situation unclear
No system size dependence at low μB
Results at high μB not in agreement (NA49, STAR)
Data on rare particles scarce at low energies
Many opportunities for experiments at NICA and FAIR !
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

23. Backup
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

24. Chemical Freeze-Out System Size Dependence: Data
LHC
ALICE: Pb—Pb at √sNN = 2.76 TeV
RHIC
STAR: beam energy scan
SPS
NA61, NA49
p/π- _
K-/π-
M. Floris, QM11
L. Kumar, QM11
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

25. X. Zhu, SQM11
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

26. Introduction The QCD Phase Diagram
Variation of √sNN
→ Different regions of phase diagram
→ Map of chemical and kinetic
freeze-out points
Limit μB → 0:
RHIC experiments
New: ALICE (LHC)
High μB:
SPS + AGS
New: STAR Beam Energy Scan (BES)
NA61 (SPS)
Future: CBM (FAIR) + MPD (NICA)
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

27. Kinetic Freeze-Out Early Decoupling
Particles with low hadronic cross section
E.g. multi-strange baryons (Ξ, Ω)
Should decouple earlier
Less affected by transverse expansion of hadronic phase
Effect visible in BW fits at RHIC and LHC
Higher Tkin and lower 〈βT〉 for Ξ and Ω than for lighter hadrons (π, K, p)
STAR: PRL92,
(2004).
N. Xu and M. Kaneta, NPA698, 306 (2002).
NA49: PRL94,
(2005).
(A) Tkin = 90 MeV
〈βT〉 = 0.5
(B) Tkin = 170 MeV
〈βT〉 = 0.2
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

28. Energy Dependence /π- and /π-Ratios
/
NA49 data
Phys. Rev. C78,
(2008)
Transport models
OK for 
Too low for 
Statistical models
Generally good
description at all
energies
|y| < 0.4
/ −
+/ −
-/
|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, (2004)
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

29. Energy Dependence ϕ Meson: Total Yields
At SPS yields not fully
described by models
UrQMD1.3 underestimates ϕ/π-ratio
but good description of ϕ yield
at lower energies
Statistical model (γs = 1) above ϕ/π-ratio
HGM: P. Braun-Munzinger et al., Nucl. Phys. A 687, 902 (2002).
NA49 data
Phys. Rev. C78, (2008)
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

30. Chemical Freeze-Out Limit μB → 0 and LHC Expectation
Freeze-out points coincide with phase boundary at RHIC and top SPS energies
Chiral phase transition from LQCD
O. Kaczmarek et al., PRD83, (2011)
P. Braun-Munzinger
and J. Stachel,
arXiv:
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

31. Chemical Freeze-Out Energy Dependence of Freeze-Out Parameters
Parameterizations of Tch and μB as function of √sNN
Freeze-out curve
J. Cleymans et al., PRC73, (2006)
Andronic et al.
Phys. Lett. B673,
142 (2009).
Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt

32. Christoph Blume NICA/JINR-FAIR Workshop, FIAS Frankfurt