system size dependence of strangeness production at the sps and rhic ags and sis
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System-size dependence of Strangeness Production at the SPS ( ... and RHIC, AGS and SIS). Claudia Höhne, GSI Darmstadt. Introduction. energy. system size. strangeness production sensitive to the phase created in A+A collisions: possible indicator for phase transition.

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system size dependence of strangeness production at the sps and rhic ags and sis

System-size dependence of Strangeness Production at the SPS( ... and RHIC, AGS and SIS)

Claudia Höhne, GSI Darmstadt



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!

  • 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


  • conclusion (I)
  • energy dependence of system-size dependence of relative strangeness production (RHIC, SPS, AGS, SIS)
  • discussion
  • conclusion (II) – open questions
s production vs system size
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:

statistical model
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]

redefine hadronization volume v
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:

cluster formation
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


As = prs2

mean area density of nn collisions
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

clustersize versus centrality
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

  • 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]

a c hadronization volume v
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
comparison with experiment
Comparison with experiment
  • experimentally, total relative s-production is not accessible:

approximate with

  • assume



rs = 0.3fm V0=4.2fm3

ms=280 MeV T=160MeV


V=V0 Npart/2

V from percolation

conclusion i
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?


comparison to rhic
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

sps 40 agev

pp NN

semicentral CC

central SiSi


"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


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

  • 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

e dependence of size dependence
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

e dep of size dependence ii
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


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?

discussion ii
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

rescattering in rqmd
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?

conclusion ii
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?
k ratio versus rapidity rhic
K/ ratio versus rapidity (RHIC)
  • BRAHMS collaboration, QM04

[D. Ouerdane, J.Phys.G: Nucl.Part.Phys.30 (2004) S1129]

discussion ii1
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?


T=146 MeV

NA49 40 AGeV