Statistical Model Predictions for p+p and Pb+Pb Collisions at LHC

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

2. 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 Heavy Ion Collisions School, Erice, Sept 18, 2008

3. T, Vb, Nb T, V, m 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 Heavy Ion Collisions School, Erice, Sept 18, 2008

4. Thermal Parameters in Pb+Pb Phys. Rev. C 73(2006) 034905 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) 034905 Grand canonical ensemble for Pb+Pb predictions Heavy Ion Collisions School, Erice, Sept 18, 2008

5. Predictions for Pb+Pb • Reliable for stable particles • Benchmark for resonances Errors: T = 170 +/- 5 MeV μB = 1 + 4 MeV Phys. Rev. C 74 (2006) 034903 - 1 All calculations with THERMUS hep-ph/0407174 Heavy Ion Collisions School, Erice, Sept 18, 2008

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

13. System size and energy dep. of cluster size • A+A: clusters smaller than fireball • RC not well defined for RC ≥ 2 fm because suppression vanishes RC= R Pb+Pb Au+Au 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 ≈ 2 - 3 fm • no precise determination for weak strangeness suppression Heavy Ion Collisions School, Erice, Sept 18, 2008

15. Extrapolation to LHC: T - mB – systematics Phys. Rev. C 73(2006) 034905 • 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 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 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 Heavy Ion Collisions School, Erice, Sept 18, 2008

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

19. Extraction of RC • Sensitivity increases with strangeness difference RC from W / p ☺ hep-ph 0808.0611 Heavy Ion Collisions School, Erice, Sept 18, 2008

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

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

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