1. Statistical Model Predictions for p+p and Pb+Pb Collisions at LHC
Ingrid Kraus
Nikhef and TU Darmstadt

2. Heavy Ion Collisions School, Erice, Sept 18, 2008
Outline
Predictions for Pb+Pb collisions at LHC
Extrapolation of thermal parameters, predictions
Experimental observables for T and μB determination
From Pb+Pb to p+p: system size dependence
Model ansatz with correlated, equilibrated clusters
Analysed data and results
Predictions for p+p collisions at LHC
Driven by initial or final state?
Summary
in Collaboration with H. Oeschler, K. Redlich, J. Cleymans, S. Wheaton
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

3. Hadron ratios in the grand canonical ensemble
large systems, large number of produced hadrons
two parameters describe particle ratios in the hadronic final state
T, V, m
T, Vb, Nb
A. Andronic,
P. Braun-Munzinger,
J. Stachel,
Nucl. Phys. A772
(2006) 167
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

4. Thermal Parameters in Pb+Pb
Phys. Rev. C 73(2006)
On the freeze-out curve:
TLHC ≈ TRHIC ≈ 170 MeV
T ≤ TC ≈ 170 MeV
μB from parametrised
freeze-out curve:
μB (√(sNN) = 5.5TeV) = 1 MeV
Phys. Rev. C 73 (2006)
Grand canonical ensemble
for Pb+Pb predictions
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

5. Heavy Ion Collisions School, Erice, Sept 18, 2008
Predictions for Pb+Pb
Reliable for stable particles
Benchmark for resonances
Errors:
T = 170 +/- 5 MeV
μB = MeV
Phys. Rev. C 74 (2006)
- 1
All calculations with THERMUS hep-ph/
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

6. T and μB dependence I: h / h ratios_
T and μB dependence I: h / h ratios
Sensitive on μB
determine μB from p/p
weakly dep. on T ☺ _
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

7. T dependence: ratios with large Dm
Ratios with larger mass differences are more sensitive
T from W / p and/or W / K ☺
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

8. T and μB dependence II: mixed ratios
Controlled by masses
Weakly dep. on μB and T
K/p
not usable for T and mB determination
good test of predictions
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

9. Canonical suppression
Canonical ensemble
small systems / peripheral collisions, low energies
suppressed phase-space for particles related to conserved charges
Stronger suppression for multi-strange hadrons
Suppression depends on strangeness content, not difference
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

10. Canonical suppression
Canonical ensemble
small systems / peripheral collisions, low energies
suppressed phase-space for particles related to conserved charges
Stronger suppression for multi-strange hadrons
Suppression depends on strangeness content, not difference
Suppressed strangeness production beyond canonical suppression
SPS √(sNN) = 17 AGeV
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

11. Modification of the model
Statistical Model approach: T and μB
Volume for yields → radius R used here
Deviations: strangeness undersaturation factor gS
Fit parameter
Alternative: small clusters (RC) in fireball (R): RC ≤ R
Chemical equilibrium in subvolumes: canonical suppression
RC free parameter
Study
p+p, C+C, Si+Si, Pb+Pb / Au+Au collisions
at SPS and RHIC energies R RC
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

12. System size and energy dep. of cluster size
Small clusters in all systems
Small system size dependence
p+p
energy dependence?
Pb+Pb / Au+Au
data consistent with saturated strangeness production
p+p C+C Si+Si Pb/Au
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

13. System size and energy dep. of cluster size
RC= R
Pb+Pb
Au+Au
A+A: clusters smaller than fireball
RC not well defined for RC ≥ 2 fm because suppression vanishes
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

14. System size and energy dep. of cluster size
RC= R
Pb+Pb
Au+Au
Particle ratios saturate at RC ≈ fm
no precise determination for weak strangeness suppression
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

15. Extrapolation to LHC: T - mB – systematics
Chemical decoupling conditions extracted from SIS up to RHIC feature common behavior
Extrapolation to LHC energy with parametrisation e.g.
Nucl. Phys. A 697 (2002) 902
Phys. Rev. C 73(2006)
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

16. System size and energy dep. of T and mB
T, μB weakly dependent on system size
p+p C+C Si+Si Pb/Au
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

17. Extrapolation to LHC: cluster size
what defines RC in p+p?
initial size of p+p system relevant
RC const
final state of large number of produced hadrons relevant
RC increases with multiplicity
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

18. Heavy Ion Collisions School, Erice, Sept 18, 2008
Prediction for p+p
significant increase of ratios at RC ≈ 1.5 fm
RC will be determined with ALICE data
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

19. Heavy Ion Collisions School, Erice, Sept 18, 2008
Extraction of RC
Sensitivity increases with strangeness difference
RC from W / p ☺
hep-ph
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

20. Heavy Ion Collisions School, Erice, Sept 18, 2008
W / p
For Pb+Pb ratio was proposed as a measure of T but …
Sensitivity on canonical suppression is much stronger than on T
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

21. Heavy Ion Collisions School, Erice, Sept 18, 2008
Summary
Pb+Pb
predictions for particle ratios with extrapolated parameters T, μB
T, μB determination with p / p and W / K or W / p ratios
p+p
predictions difficult due to unknown degree of canonical suppression
Cluster radius RC from data _
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008

22. Heavy Ion Collisions School, Erice, Sept 18, 2008
Data and fits
Ingrid Kraus, Nikhef
Heavy Ion Collisions School, Erice, Sept 18, 2008