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

Claudia Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne Critical Point and Onset of Deconfinement, Bergen, March/ April 2005 ss 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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 Höhne 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