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System-Size Dependence of Strangeness Production in Heavy Ion Collisions

Explore the relationship between system size and relative strangeness production in A+A collisions at various energies, utilizing percolation and statistical models for analysis and comparison. Study the volume dependence and hadronization processes to understand the mechanisms driving strangeness enhancement. Gain insights into phase transitions and collective volume formation through cluster analysis. Compare results with experimental data and discuss implications for multi-strange particles and future research directions.

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System-Size Dependence of Strangeness Production in Heavy Ion Collisions

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  1. System-size dependence of Strangeness Production at the SPS( ... and RHIC, AGS and SIS) Claudia Höhne, GSI Darmstadt

  2. Introduction energy system size strangeness production sensitive to the phase created in A+A collisions: possible indicator for phase transition maximum in energy dependence observed complementary information from the system-size dependence!

  3. Outline • data – system-size dependence of relative strangeness production at SPS: • central C+C, Si+Si, Pb+Pb collisions at 158 AGeV • concentrate on s=1 • model – percolation model for quantitative description of data (hep-ph/0507276) • conclusion (I) • energy dependence of system-size dependence of relative strangeness production (RHIC, SPS, AGS, SIS) • discussion • conclusion (II) – open questions

  4. s-production vs system-size pp (Lit.) CC, SiSi 15%, 12% SS (NA35) 2% PbPb 5% fast increase for small systems, saturation from Npart > 60 on! [NA49, PRL 94, 052301 (2005)] 158 AGeV lines are to guide the eye:

  5. Statistical model strangeness enhancement due to release of canonical strangeness suppression suppression factor h calculated for a certain volume V, common assumption: → qualitatively in agreement with data → quantitatively in disagreement: saturation is reached much too early (Npart ~ 9) define V more carefully [Tounsi and Redlich, J. Phys. G: Nucl. Part. Phys 28 (2002) 2095]

  6. Redefine hadronization volume V • microscopic model of A+A collisions → high density of collisions/strings • assign a transverse extension to the individual NN collisions ("string-radius"), assume that due to the overlap of these strings clusters of highly excited and strongly interacting matter are formed; strings/collisions no longer independent • assume independent hadronization of these clusters • particle compositions (here: relative strangeness production) calculated from the statistical model (as it is so successful for central AuAu/ PbPb) • main purpose: calculate system-size dependence of relative strangeness production in A+A collisions (at 158 AGeV) percolation model: cluster formation statistical model: cluster hadronization lines are to guide the eye:

  7. Cluster formation strings associated with NN collision are given a transverse size As distributed in overlap zone A of a A+A collision assumption: overlapping strings form clusters (size AC): percolation model AC As = prs2

  8. Mean area density of NN collisions 2 dimensional projection of N+N collisions (SiSi at 158 AGeV < 1fm penetration time) VENUS model (calculation for pp, CC, SiSi, SS, centrality dependent PbPb) (small) geometry effect between central (light) A+A and peripheral Pb+Pb

  9. Clustersize versus centrality combine the two calculations → clustersize for different system sizes! small systems ("pp"): basically one small cluster/ string large systems ("central PbPb"): one large cluster and a certain probability for small ones in the outer region of the overlap zone intermediate systems: several clusters of different size

  10. Hadronization • assume: clusters form coherent entity → hadronization volume V • apply statistical model for calculation of relative strangeness production () of the hadronization volume V • here: only goal is relative strangeness production • here: calculation performed for strange quarks in a quark phase, parameters are T, ms • note: almost same behaviour for hadron gas with T~161 MeV, B~260 MeV, V0~7fm3 V0 hadronization volume of pp [Rafelski, Danos, PLB 97 (1980) 279]

  11. AC→ hadronization volume V • in order to apply the statistical hadronization scheme, the clustersizes AC have to be transformed to hadronization volumes Vh → factor that accounts for the (transverse) expansion until hadronization and for the longitudinal dimension at hadronization • compare with the situation in a single NN collision: hadronization volume ~ V0 (V0 nucleon volume) • here: leave V0 as adjustable parameter

  12. Comparison with experiment • experimentally, total relative s-production is not accessible: approximate with • assume [hep-ph/0507276] parameters: rs = 0.3fm V0=4.2fm3 ms=280 MeV T=160MeV a=0.18 V=V0 Npart/2 V from percolation

  13. Conclusion (I) • at top SPS energy, the system-size dependence of relative strangeness production can be quantitatively understood as being due to the release of canonical strangeness suppression if only the volume is chosen appropriately (percolation ansatz!): • in particular for intermediate systems several clusters of different size • even in central Pb+Pb certain probability of pp-like clusters • important: formation of collective volumes of increasing size same shape of increase for partonic or hadronic phase multi-strange particles? → future other variables? → see application of percolation model to fluctuations etc. from Pajares et al, Armesto et al,... other energies? RHIC, SPS (40 GeV), AGS, SIS

  14. Comparison to RHIC • PHENIX: K+/+ ratio at midrapidity [PRC 69 (2004) 034909] • assume K+/+ ratio at midrapidity to be representative for the total relative s-production BRAHMS: ratio nearly independent on rapidity [JPG 30 (2004) S1129] • T=164 MeV to adjust for lower total s-enhancement CuCu 200 GeV AuAu 200 GeV PbPb 17.3 GeV

  15. SPS 40 AGeV pp NN semicentral CC central SiSi PbPb "geometry" effect comparing central collisions of small nuclei with peripheral Pb+Pb at the same Nwound collision densities in central A+A different to peripheral PbPb at same Nwound P. Dinkelaker, NA49, SQM04 [JPG 31 (2005) S1131] 40 GeV beam energy 4 yields

  16. AGS AGS (E802) [PRC 60 (1999) 044904] • strong geometry effect for smaller systems (however: different energy! – might change steepness of increase in addition) • continuous rise towards central AuAu 4 yields

  17. SIS • SIS: KAOS experiment, Ebeam=1.5 AGeV [JPG 31 (2005) S693] open symbols: Ni+Ni closed symbols Au+Au • smaller geometry effect compared to AGS? 200 Apart 4 yields

  18. E-dependence of size dependence K+ production taken as representative of total s-production normalize to  - (available for all; AGS: F.Wang, private communication (1999)) continuous change with energy? later saturation for lower energies PHENIX s = 200 GeV NA49 Ebeam = 40 AGeV E802 Ebeam = 11.1 AGeV KAOS Ebeam = 1.5 AGeV PHENIX yields at midrapidity, others total yields all normalized to most central ratio

  19. E-dep. of size dependence (II) • ... normalize all to Nwound (central bin of KAOS – two normalizations shown) • different calculation of Nwound in particular for AGS data (AGS: Npart from spectator energy, others: Glauber model) → (clear) difference for lower/ higher energies? all normalized to most central ratio ... KAOS yields adjusted to AGS

  20. Discussion saturation of relative strangeness production for all energies – or only for higher?? role of pions in PbPb/ AuAu?: usage of small systems instead better defined? calculation of Nwound?

  21. Discussion (II) • statistical model description as discussed for top SPS, RHIC holds for all energies → SIS, AGS reach grandcanonical limit (if!) only in central Au+Au collisions (usage of grand canonical ensemble in statistical model fits justified?) → stat. model: lower temperature, higher B slows down increase → still rather small clusters needed for SIS, AGS → lower collision densities (longer penetration time, lower energy) → lower probability for cluster formation ? → formation of clusters from hadrons more difficult than from strings → geometry effect due to different densities ..... any correlation to the phase of matter? • purely hadronic rescattering scenario → with Nwound the reaction time increases, equilibrium reached for central Au+Au collisions? → geometry effect due to different densities

  22. Rescattering in RQMD different scenario at lower energies? F. Wang et al. (RQMD), PRC 61 (2000) 064904: continuous rise of K/ ratio due to rescattering in the hadron gas (effect of ropes negligible for AGS) with Npart the reaction time increases, saturation (equilibrium) reached?

  23. Conclusion (II) • RHIC data can be easily understood within the same picture introduced in the first part of this talk • system-size dependence at lower energies? • systematic change is visible (20, 30 AGeV data from NA49 to come!) • unfortunately: data situation unclear (normalization?) • saturation of relative strangeness production for all energies?? • how strong is the geometry effect for smaller systems? • all explainable within same picture? • can the energy dependence of the system-size dependence tell us something about the scenario?

  24. K/ ratio versus rapidity (RHIC) • BRAHMS collaboration, QM04 [D. Ouerdane, J.Phys.G: Nucl.Part.Phys.30 (2004) S1129]

  25. Discussion (II) percolation model + statistical hadronization: • only changing T to 146 AGeV is not sufficient to explain the data at 40 AGeV (small systems? geometry effect!) simplifying assumptions in model: • different definition of volumes needed? e.g. 2-dimensional projection not justified anymore? usage of 3d-densities and cluster formation needed? • centrality dependent parameters for statistical model? PHENIX data T=146 MeV NA49 40 AGeV

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