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

Claudia Höhne Strangeness in Collisions workshop, BNL, February 16-17, 2006

Introduction

• maximum in energy dependence

observed

• complementary information from

the system-size dependence!

energy

system size

KKEs

2

• strangeness production sensitive to the phase created in A+A collisions:

possible indicator for phase transition


Outline

• 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

(hep-ph/0507276)

• 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

• fast increase for small systems, saturation from Npart > 60 on!

pp (Lit.)

CC, SiSi 15%, 12%

SS (NA35) 2%

PbPb 5%

2

1

40exp partN

ba

[NA49, PRL 94, 052301 (2005)]

lines are to guide the eye:

158 AGeV


Statistical model• strangeness enhancement due to release of canonical strangeness suppression

• suppression factor calculated for a certain volume V, common assumption: partN

VV

20

KKEs

2

define V more carefully

[Tounsi and Redlich, J. Phys. G: Nucl. Part. Phys 28 (2002) 2095]

→ qualitatively in agreement with data

→ quantitatively in disagreement: saturation

is reached much too early (Npart ~ 9)


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


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 = rs2

AC


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

• 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


Hadronization

• 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]


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

20

sCh r

VAV


Comparison with experiment

• experimentally, total relative s-production is not accessible:

approximate with

• assume

KKEs

2

)()( hwoundS VaNE

parameters:

rs = 0.3fm V0=4.2fm3

ms=280 MeV T=160MeV

a=0.18

V=V0 Npart/2

V from percolation

[hep-ph/0507276]


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? RHIC, SPS (40 GeV), AGS, SIS


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

/K

CuCu 200 GeV

AuAu 200 GeV

PbPb 17.3 GeV


SPS 40 AGeV

P. Dinkelaker, NA49, SQM04

[JPG 31 (2005) S1131]

• "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

40 GeV beam energy

pp NN

semicentral CC

central SiSi

PbPb

4 yields


AGS

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


200 Apart

SIS

• 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?

4 yields


E-dependence of size dependence

PHENIX s = 200 GeV

NA49 Ebeam = 40 AGeV

E802 Ebeam = 11.1 AGeV

KAOS Ebeam = 1.5 AGeV

• 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 yields at midrapidity,

others total yields

all normalized to most central ratio


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


Discussion

• 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)

• 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• 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)

• 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)

• BRAHMS collaboration, QM04

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


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

PHENIX data

NA49 40 AGeV

system-size dependence of strangeness production at the sps ( ... and rhic, ags and sis)

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