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

2. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 20072 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 and energy 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, NikhefLast call for predictions workshop, CERN, May 30, 20073 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, NikhefLast call for predictions workshop, CERN, May 30, 20074 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, NikhefLast call for predictions workshop, CERN, May 30, 20075 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, NikhefLast call for predictions workshop, CERN, May 30, 20076 T and μ B dependence I: mixed ratios Controlled by masses Weakly dep. on μ B and T –μ B term cancels –larger contributions from resonances at higher T

7. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 20077 T and μ B dependence I: mixed ratios Controlled by masses Weakly dep. on μ B and T –μ B term cancels –larger contributions from resonances at higher T

8. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 20078 T and μ B dependence I: mixed ratios Controlled by masses Weakly dep. on μ B and T –μ B term cancels –larger contributions from resonances at higher T K/  –not usable for T and  B determination –good test of predictions

9. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 20079 T and μ B dependence II: h/h ratios Sensitive on μ B – μ S opposite trend of μ B –determine μ B from p/p weakly dep. on T _ _ ☺

10. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200710 T dependence: ratios with large mass differences ☺ Ratios with larger mass differences are more sensitive T from  and/or  K

11. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200711 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

12. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200712 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

13. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200713 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

14. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200714 System size and energy dependence of the 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

15. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200715 System size and energy dependence of the 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

16. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200716 System size and energy dependence of the 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

17. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200717 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

18. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200718 System size and energy dependence of T and  B p+p C+C Si+Si Pb/Au T, μ B weakly dependent on system size

19. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200719 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

20. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200720 Prediction for p+p significant increase of ratios at R C ≈ 1.5 fm K /  and  behave differently –multistrange hadrons suffer stronger suppression R C will be determined with ALICE data

21. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200721 Extraction of R C Particle ratios w/o strangeness are insensitive to R C Sensitivity increases with strangeness difference R C from  ☺

22. Ingrid Kraus, NikhefLast call for predictions workshop, CERN, May 30, 200722 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