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

2. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20082 Outline Predictions for Pb+Pb collisions at LHC –Extrapolation of thermal parameters, predictions –Experimental observables for T and μ B 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

3. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20083 Hadron ratios in the grand canonical ensemble Grand canonical ensemble –large systems, large number of produced hadrons –two parameters describe particle ratios in the hadronic final state A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl. Phys. A772 (2006) 167 T, V,  T, V b, N b

4. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20084 On the freeze-out curve: T LHC ≈ T RHIC ≈ 170 MeV T ≤ T C ≈ 170 MeV μ B from parametrised freeze-out curve: μ B (√(s NN ) = 5.5TeV) = 1 MeV Phys. Rev. C 73 (2006) 034905 Grand canonical ensemble for Pb+Pb predictions Thermal Parameters in Pb+Pb Phys. Rev. C 73(2006) 034905

5. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20085 Predictions for Pb+Pb Reliable for stable particles Benchmark for resonances Errors: T = 170 +/- 5 MeV μ B = 1 + 4 MeV Phys. Rev. C 74 (2006) 034903 - 1 All calculations with THER MUS hep-ph/0407174

6. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20086 T and μ B dependence I: h / h ratios Sensitive on μ B determine μ B from p/p weakly dep. on T _ _ ☺

7. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20087 T dependence: ratios with large  m ☺ Ratios with larger mass differences are more sensitive T from  and/or  K

8. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20088 T and μ B dependence II: mixed ratios Controlled by masses Weakly dep. on μ B and T K/  –not usable for T and  B determination –good test of predictions

9. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 20089 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

10. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200810 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 √(s NN ) = 17 AGeV

11. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200811 Modification of the model Statistical Model approach: T and μ B –Volume for yields → radius R used here Deviations: strangeness undersaturation factor  S –Fit parameter Alternative: small clusters (R C ) in fireball (R): R C ≤ R –Chemical equilibrium in subvolumes: canonical suppression –R C free parameter Study –p+p, C+C, Si+Si, Pb+Pb / Au+Au collisions –at SPS and RHIC energies R RCRC

12. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200812 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

13. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200813 System size and energy dep. of cluster size A+A: clusters smaller than fireball R C not well defined for R C ≥ 2 fm because suppression vanishes R C = R Pb+Pb Au+Au

14. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200814 System size and energy dep. of cluster size Particle ratios saturate at R C ≈ 2 - 3 fm –no precise determination for weak strangeness suppression Pb+Pb Au+Au R C = R

15. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200815 Extrapolation to LHC: T -  B – 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) 034905

16. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200816 System size and energy dep. of T and  B p+p C+C Si+Si Pb/Au T, μ B weakly dependent on system size

17. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200817 Extrapolation to LHC: cluster size what defines R C in p+p? initial size of p+p system relevant –R C const final state of large number of produced hadrons relevant –R C increases with multiplicity

18. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200818 Prediction for p+p significant increase of ratios at R C ≈ 1.5 fm R C will be determined with ALICE data

19. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200819 Extraction of R C Sensitivity increases with strangeness difference R C from  ☺ hep-ph 0808.0611

20. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200820  For Pb+Pb ratio was proposed as a measure of T but … Sensitivity on canonical suppression is much stronger than on T

21. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200821 Summary Pb+Pb –predictions for particle ratios with extrapolated parameters T, μ B –T, μ B determination with p / p and  / K or  /  ratios _ p+p –predictions difficult due to unknown degree of canonical suppression –Cluster radius R C from data

22. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200822 Data and fits

23. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200823 Data and fits II

24. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200824 Tables from paper

25. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200825 Resonance Contribution to p/p Ratio not affected by feeding –net baryon number is conserved _

26. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200826 Resonance Contribution to K and 

27. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200827 Resonance Decays  no resonance contribution  – 50% from feed-down –both exhibit same T dependence K decay exceeds thermal at LHC  –thermal production ≈ constant –resonance contribution dominant 75% of all  from resonances p/p primary ≈ p/p decay __

28. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200828 Sensitivity on T Thermal –K /  and  /  have same T dependence –sensitivity increases with mass difference Decay contribution –lighter particles are stronger affected –increasing feed-down with increasing T Relative variation of R per 1MeV change of T

29. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200829 More SPS and RHIC 200 GeV Data

30. Ingrid Kraus, NikhefQGP workshop, Erice, Sept 18, 200830 Model setting with  S  S –sensitive on data sample –increase with size –increase with energy