System-size dependence of strangeness production, canonical strangeness suppression, and percolation Claudia Hhne, GSI Darmstadt Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Outline introductiondata (central A+A, top SPS energy) statistical model percolation model percolation + statistical model discussionresults input parameters/ assumptions s transfer to minimum bias Pb+Pb RHIC energies multistrange particles other system-size dependent variables? summary Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Introduction energy system sizerelative 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! [NA49, M. Gazdzicki, QM04] Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Data system-size dependence of relative strangeness production fast increase with system size saturation reached at about N part =60 * pp CC, SiSi SS (2% central) PbPb (5% central) lines are to guide the eye (exponential function) * 80% of full enhancement between pp and PbPb 158 AGeV 200 AGeV 158 AGeV [NA49, PRL 94 (2005) ] Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Statistical model [Tounsi and Redlich, J. Phys. G: Nucl. Part. Phys 28 (2002) 2095] statistical model: canonical strangeness suppression qualitative agreement quantitatively in disagreement: 80% of enhancement reached at N part ~ 9 (s=1) calculated for a certain V common assumption V N part E s [NA49, PRL 94 (2005) ] define V more carefully! Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Percolation model [Satz, hep-ph/ )] 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 Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 The Model 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 Separate collision process/ particle production into two independent steps: Any effects of interactions in the final hadronic expansion stage are neglected. Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April once more: step 1 percolation calculation: clustersize vs density relate density to N wound step 2 hadronization of clusters canonical strangeness suppression from statistical model N wound V correlation EsEs combine: E s vs. N wound Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 step 1 VENUS: N wound ( VENUS simulations (2d)* collision density < in dependence on N wound density distribution (common profile used) coll2d (N wound ) = percolation * simplification: 2d calculation in particular for light systems penetration time of nuclei < 1fm/c no further subdivision of longitudinal dimension Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 step 1 percolation calculation 2d: projection of collisions to transverse plane distribute strings/ collisions effective r string = 0.3 fm * form clusters from overlapping strings VENUS: 2d density distribution of strings/ collisions * lattice-QCD: see e.g. argument from Satz in PLB 442 (1998) 14 A s = r s 2 A AcAc Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 step 1 percolation calculation (II) mean cluster size 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 Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 areasize distribution combine N wound ( ) and A c ( ) areasize distribution vs N wound even for higher densitys small clusters are present ! Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 step 2 hadronization of clusters correlate relative s-production to clustersize statistical model: strangeness suppression factor (V) [Rafelski and Danos, Phys. Lett. B97 (1980) 279] r 0 nucleon radius s-content in partonic/ hadronic phase? in practice: both assumptions yield similar result s=1 Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 combine results & compare to data data well described! r s = 0.3fm, V h = 3.8fm 3 experimentally Wroblewski factor s not accessible: approximate by E s, assume E s V N wound calculation taking clustersize distribution into account Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 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 Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Discussion sensitivity of model to assumptions/ input/ parameters? s ? 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? Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Assumptions/ input assumptions/ input/ parameters for this model: 2dimensional calculation essential features already covered! scaling parameter a: E s = a determined by data percolation calculation: r s, V h V h total enhancement, r s shape standard (r s =0.3fm, V h =3.8 fm 3 ) r s =0.2fm, V h =3.1 fm 3 r s, V h not uniquely defined, can be played against each other to certain extend Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Assumptions/ input (II) statistical model: (V,T,m s ) change in m s can e.g. be accomplished by V h standard (T=160 MeV, m s =280 MeV) T=160 MeV, m s =150 MeV, V h =2.7 fm 3 Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Assumptions/ input (III) collision density distribution only very slight change standard (2d density distribution) uniform distribution (V h =4 fm 3 ) there is a certain sensitivity to parameter variation several reasonable pairs can be found to describe data always: main effect comes from clustersize distribution! Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 ss here: any possible strangeness undersaturation ( s ) neglected total increase of relative strangeness production adjusted with V h however: note similar ansatz in Becattini et al., PRC 69 (2004) Manninen, SQM04 two component model: fix s =1 but allow for N s single collisions similar to percolation result! Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Transfer: minimum bias Pb+Pb main difference to central collisions: slower increase of collision density A(N wound ) more difficult to define increase in E s slower (observed in experiment!) grey area: A defined as geometrical overlap zone of colliding nuclei using R enclosing 90% (50%) of nuclear density distribution in qualitative agreement with preliminary NA49 data Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 [PHENIX, PRC 69 (2004) ] midrapidity Transfer: other energies (RHIC) assume that same s-production mechanism holds for top-SPS and RHIC energies transfer calculation only change: calculate N wound ( ), A(N wound ) for Au+Au at different centralities Cu+Cu: basically same dependence expected (dashed line)! AGS energies more complicated? hadronic scenario, rescattering [PHENIX, PRC 69 (2004) ] midrapidity Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 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 E s for s=2,3 needed Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 Transfer: multistrange particles (II) [NA57, nucl-ex/ (QM04)] s=2: s=3: ( + )/N wound should be comparable NA57 data normalization to pBe (errors!) characteristic features also captured for s=2,3 Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 percolation & system-size dependence percolation ansatz: connect system-size dependence of variables with geometrical properties of the collision system increase of V cluster relate physical properties to V cluster strangeness production several clusters in small systems fluctuations! ? strangeness ? Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 and vs. system-size and depend on the size of the cluster (and string density) therefore p t and N ch changes with cluster size [Braun, del Moral, Pajares, PRC 65, (2002)] [Dias de Deus, Ferreiro, Pajares, Ugoccioni, hep-ph/ ] Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April fluctuations Ferreiro, del Moral, PajaresPRC 69, (2004) correlate clustersize to : 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 fluctuations Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 multiplicity fluctuations ? same picture should be applicable here! [Mrowczynski, Rybczynski, Wlodarczyk, PRC 70 (2004) ] relate multiplicity and fluctuations strangeness fluctuations?? NA49 preliminary [Rybczynski for NA49, J.Phys.Conf.Ser 5 (2005) 74] Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 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, with centrality fluctuations ( multiplicity fluctuations ?) J/ suppression Claudia Hhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 J/ suppression Nardi, Satz e.g. PLB 442 (1998) 14 deconfinement in clusters J/ suppression