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Claudia Höhne, GSI Darmstadt

System-size dependence of strangeness production, canonical strangeness suppression, and percolation. Claudia Höhne, GSI Darmstadt. Outline. introduction data (central A+A, top SPS energy) statistical model percolation model percolation + statistical model discussion results

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Claudia Höhne, GSI Darmstadt

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  1. System-size dependence of strangeness production,canonical strangeness suppression, and percolation Claudia Höhne, GSI Darmstadt

  2. Outline • introduction data (central A+A, top SPS energy) • statistical model • percolation model • percolation + statistical model • discussion results • input parameters/ assumptions • gs • transfer to minimum bias Pb+Pb • RHIC energies • multistrange particles • other system-size dependent variables? • summary

  3. energy system size Introduction [NA49, M. Gazdzicki, QM04] • relative strangeness production as possible indicator for the transition from confined to deconfined matter • energy dependence • maximum at ~ 30 AGeV beam energy • system-size variation • complementary information!

  4. Data pp CC, SiSi SS (2% central) PbPb (5% central) 158 AGeV 158 AGeV 200 AGeV 158 AGeV system-size dependence of relative strangeness production [NA49, PRL 94 (2005) 052301] • fast increase with system size • saturation reached at about Npart=60 * * 80% of full enhancement between pp and PbPb lines are to guide the eye (exponential function)

  5.   Es [NA49, PRL 94 (2005) 052301] Statistical model statistical model: canonical strangeness suppression  • qualitative agreement • quantitatively in disagreement: • 80% of enhancement reached at • Npart ~ 9 (s=1) •  calculated for a certain V • common assumption V  Npart define V more carefully! [Tounsi and Redlich, J. Phys. G: Nucl. Part. Phys 28 (2002) 2095]

  6. [Satz, hep-ph/0212046)] Percolation model • microscopic picture of A+A collision: • subsequent N+N collisions take place in immediate space-time density • still individual „collisions“/ individual hadronization? • suppose that overlapping collisions (strings) form clusters •  percolation models

  7. The Model Separate collision process/ particle production into two independent steps: • 1) Formation of coherent clusters: “correlation volume“ • percolation of collisions/ strings • 2) Hadronization of clusters  relative strangeness production • statistical model (canonical strangeness suppression) • assume that „correlation volumes“ from percolation calculation can be identified with volume used in the statistical model Any effects of interactions in the final hadronic expansion stage are neglected.

  8. Es Vcorrelation Nwound ... once more: • step 1 – percolation calculation: • clustersize vs density • relate density to Nwound • step 2 – hadronization of clusters • canonical strangeness suppression from statistical model combine: Es vs. Nwound

  9. step 1 – VENUS: Nwound (r) * simplification: 2d calculation in particular for light systems penetration time of nuclei < 1fm/c  no further subdivision of longitudinal dimension • VENUS simulations (2d)* • collision density <r> in dependence on Nwound • density distribution (common profile used) • rcoll2d (Nwound) = rpercolation

  10. VENUS: step 1 – percolation calculation • 2d: projection of collisions to transverse plane • distribute strings/ collisions • effective rstring = 0.3 fm * • form clusters from overlapping strings 2d density distribution of strings/ collisions As = prs2 A Ac * lattice-QCD: see e.g. argument from Satz in PLB 442 (1998) 14

  11. step 1 – percolation calculation (II) • mean cluster size <Ac> rises steeply with density • using density distribution of collisions weakens rise compared to uniform distribution uniform distribution of strings density distribution (VENUS) transverse area A = geometrical overlap zone of colliding nuclei using R enclosing 90% of nuclear density distribution

  12.  areasize distribution combine Nwound(r) and Ac(r)  areasize distribution vs Nwound even for higher densitys small clusters are present !

  13. r0 nucleon radius step 2 – hadronization of clusters • correlate relative s-production to clustersize •  statistical model: strangeness suppression factor h(V) [Rafelski and Danos, Phys. Lett. B97 (1980) 279] s-content in partonic/ hadronic phase? in practice: both assumptions yield similar result s=1

  14. V  Nwound calculation taking clustersize distribution into account combine results & compare to data experimentally Wroblewski factor ls not accessible: approximate by Es, assume Es  data well described! rs = 0.3fm, Vh = 3.8fm3

  15. Summary (I) • good description of data with physically reasonable parameters • essential for good description of data: take clustersize distribution into account, not only mean values •  makes all the difference! (steep increase of (V)) • statistical model can also be successfully applied! • even if partonic scenario is used for calculation of (V), no real statement concerning the nature of the „correlation volumes“ is made – only that s-production is correlated to clustersize plausible: same nature as in central Pb+Pb but smaller size in e.g. C+C • p+p collisions – strings, Pb+Pb collisions – essentially one large cluster • A+A collisions with small A, e.g. C+C: • several independent clusters of small/ medium size

  16. Discussion • sensitivity of model to assumptions/ input/ parameters? • gs ? • transfer to other systems (s=1): minimum bias Pb+Pb at 158 AGeV • RHIC energies • multistrange particles? • percolation ansatz  relate system-size dependence of s-production to geometrical properties • can the same ansatz be used for the system-size dependence of other variables?

  17. rs, Vh not uniquely defined, can be played against each other to certain extend standard (rs=0.3fm, Vh=3.8 fm3) rs=0.2fm, Vh=3.1 fm3 Assumptions/ input • assumptions/ input/ parameters for this model: • 2dimensional calculation  essential features already covered! • scaling parameter a: Es = a   determined by data • percolation calculation: rs, Vh  Vh total enhancement, rs shape

  18. standard (T=160 MeV, ms=280 MeV) T=160 MeV, ms=150 MeV, Vh=2.7 fm3 Assumptions/ input (II) • statistical model: (V,T,ms)  change in ms can e.g. be accomplished by Vh

  19. Assumptions/ input (III) • collision density distribution  only very slight change • there is a certain sensitivity to parameter variation • several reasonable pairs can be found to describe data • always: main effect comes from clustersize distribution! standard (2d density distribution) uniform distribution (Vh=4 fm3)

  20. similar to percolation result! gs • here: any possible strangeness undersaturation ( gs) neglected • total increase of relative strangeness production adjusted with Vh however: note similar ansatz in Becattini et al., PRC 69 (2004) 024905 Manninen, SQM04  two component model: fix gs=1 but allow for Ns single collisions

  21. Transfer: minimum bias Pb+Pb main difference to central collisions: slower increase of collision density A(Nwound) more difficult to define  increase in Es slower (observed in experiment!) in qualitative agreement with preliminary NA49 data grey area: A defined as geometrical overlap zone of colliding nuclei using R enclosing 90% (50%) of nuclear density distribution

  22. [PHENIX, PRC 69 (2004) 034909] [PHENIX, PRC 69 (2004) 034909] midrapidity midrapidity Transfer: other energies (RHIC) • assume that same s-production mechanism holds for top-SPS and RHIC energies • transfer calculation • only change: calculate Nwound(r), A(Nwound) for Au+Au at different centralities • Cu+Cu: basically same dependence expected (dashed line)! • AGS energies more complicated? • hadronic scenario, rescattering

  23. Transfer: multistrange particles • in principle simple to extend: • however: here a calculation for a partonic scenario is used • for translation to hadronic yields some kind of „coalescence“ assumption needed • calculation for canonical strangeness suppression for all s=1,2,3 particles • definition of Es for s=2,3 needed

  24. Transfer: multistrange particles (II) • s=2: X, f • s=3: (W-+W+)/Nwound should be comparable • NA57 data – normalization to pBe (errors!) characteristic features also captured for s=2,3 [NA57, nucl-ex/0403036 (QM04)]

  25. percolation & system-size dependence • percolation ansatz: • connect system-size dependence of variables with geometrical properties of the collision system • increase of Vcluster •  relate physical properties to Vcluster • strangeness production • <Nch> • <pt> • several clusters in small systems • fluctuations! <pt> <Nch> ? strangeness ?

  26. <pt> and <Nch> vs. system-size <pt> and <Nch> depend on the size of the cluster (and string density) therefore pt and Nch changes with cluster size [Dias de Deus, Ferreiro, Pajares, Ugoccioni, hep-ph/0304068] [Braun, del Moral, Pajares, PRC 65, 024907 (2002)]

  27. <pt> - fluctuations • Ferreiro, del Moral, Pajares PRC 69, 034901 (2004) • correlate clustersize to <pt>: • Schwinger mechanism for single strings  increase with clustersize • p+p and Pb+Pb: • small fluctuations because essentially one system exists: single string or one large cluster • in between: many differently sized clusters with (strongly) varying <pt>  fluctuations

  28. multiplicity fluctuations ? NA49 preliminary same picture should be applicable here! [Mrowczynski, Rybczynski, Wlodarczyk, PRC 70 (2004) 054906] relate multiplicity and <pt> fluctuations [Rybczynski for NA49, J.Phys.Conf.Ser 5 (2005) 74] strangeness fluctuations??

  29. Summary • successful description of relative strangeness production in dependence on the system-size for central A+A collisions at 158 AGeV beam energy by combining a percolation calculation with the statistical model • essential: take clustersize distribution into account (not only mean values!) •  p+p collisions – strings, Pb+Pb collisions – essentially one large cluster •  A+A collisions with small A, e.g. C+C: • several independent clusters of small/ medium size • this picture can successfully be transfered to minimum bias Pb+Pb at 158 AGeV, centrality dependent Au+Au at RHIC (200 AGeV), multistrange particles • percolation model also successful for describing system-size dependence of other variables: • increase of <pt> , <Nch> with centrality • <pt> fluctuations ( multiplicity fluctuations ?) • J/ suppression

  30. J/ – suppression Nardi, Satz e.g. PLB 442 (1998) 14 deconfinement in clusters  J/ – suppression

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