System-size dependence of strangeness production, canonical strangeness suppression, and percolation

1
System-size dependence of strangeness
production,canonical strangeness suppression,
and percolation

• Claudia Höhne, GSI Darmstadt

2
Outline

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

3
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 Npart60

80 of full enhancement between pp and PbPb
lines are to guide the eye (exponential
function)
5
Statistical model
statistical model canonical strangeness
suppression ?

• qualitative agreement
• quantitatively in disagreement
• 80 of enhancement reached at
• Npart 9 (s1)
• ? 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
Percolation model

• microscopic picture of AA collision
• subsequent NN 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
... 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
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step 1 VENUS Nwound (r)
simplification 2d calculation in particular
for light systems penetration time of nuclei lt
1fm/c ? no further subdivision of longitudinal
dimension

• VENUS simulations (2d)
• collision density ltrgt in dependence on Nwound
• density distribution (common profile used)

• rcoll2d (Nwound) rpercolation

10
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
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step 1 percolation calculation (II)

• mean cluster size ltAcgt 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
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? areasize distribution
combine Nwound(r) and Ac(r) ? areasize
distribution vs Nwound even for higher densitys
small clusters are present !
13
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
s1
14
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
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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 PbPb but
  smaller size in e.g. CC
• pp collisions strings, PbPb collisions
  essentially one large cluster
• AA collisions with small A, e.g. CC
• several independent clusters of small/ medium
  size

16
Discussion

• sensitivity of model to assumptions/ input/
  parameters?
• gs ?
• transfer to other systems (s1) minimum bias
  PbPb 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
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
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 (Vh4 fm3)
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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 gs1 but allow for Ns single
collisions
21
Transfer minimum bias PbPb
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
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 AuAu at
  different centralities
• CuCu 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 s1,2,3 particles
• definition of Es for s2,3 needed

24
Transfer multistrange particles (II)

• s2 X, f
• s3 (W-W)/Nwound should be comparable
• NA57 data normalization to pBe (errors!)

characteristic features also captured for s2,3
NA57, nucl-ex/0403036 (QM04)
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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
• ltNchgt
• ltptgt
• several clusters in small systems
• fluctuations!
• ltptgt
• ltNchgt ?
• strangeness ?

26
ltptgt and ltNchgt vs. system-size
ltptgt and ltNchgt 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
ltptgt - fluctuations

• Ferreiro, del Moral, Pajares PRC 69, 034901
  (2004)
• correlate clustersize to ltptgt
• Schwinger mechanism for single strings ?
  increase with clustersize
• pp and PbPb
• small fluctuations because essentially one
  system exists single string or one large cluster
• in between many differently sized clusters with
  (strongly) varying ltptgt ? fluctuations

28
multiplicity fluctuations ?
NA49 preliminary
same picture should be applicable
here! Mrowczynski, Rybczynski, Wlodarczyk, PRC
70 (2004) 054906 relate multiplicity and ltptgt
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 AA 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!)
• ? pp collisions strings, PbPb collisions
  essentially one large cluster
• ? AA collisions with small A, e.g. CC
• several independent clusters of small/ medium
  size

• this picture can successfully be transfered to
  minimum bias PbPb at 158 AGeV, centrality
  dependent AuAu at RHIC (200 AGeV), multistrange
  particles

• percolation model also successful for describing
  system-size dependence of other variables
• increase of ltptgt , ltNchgt with centrality
• ltptgt fluctuations (? multiplicity fluctuations
  ?)
• J/? suppression

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