Helmut Oeschler Darmstadt University of Technology

Helmut Oeschler

Darmstadt University of Technology

Centrality Dependence of Strange Particle Yieldsfrom SIS up to RHIC

Brookhaven Nat. Lab., February 17th, 2006

Observations from SIS up to RHIC:

Do particle ratios change with centrality?

Strange/non-strange particles?

Are periph. PbPb collisions and central SiSi the same or very similar?

Interpretations:

What do we expect based on our present knowledge?

SIS:

Ni+Ni and Au+Au

1.5 A GeVA. Förster, F. Uhlig, .PRL 91 (2003) 152301KaoS Coll.

Rise of K+ and K- similar

At the same Apart, Ni+Ni central and Au+Au periph. similar

AGS

E802

PRC 60 (1999)

K+ and K- similar rise

Periph. AuAu very different from SiAl.

SPS NA49 Coll.You have the choice!

0

0.1

0.2

0.3

0.4

0 100 200 300 400

<Nwound>

<K+

>/<N

wo

un

d>

CCSiSiSSPbPb

0

0.05

0.1

0.15

0.2

0 100 200 300 400

Npart

K+/

CCSiSiSSPbPb

C. Höhne, PhD thesis

K+ and K- very similar

0

0.05

0.1

0.15

0.2

0 100 200 300 400

<Nwound>

<K- >

/<N

wo

un

d>CCSiSiSSPbPb

0

0.1

0.2

0.3

0.4

0 100 200 300 400

<Nwound>

<K+

>/<

Nw

ou

nd>

CCSiSiSSPbPb

Phenix NP A757 (2005)

K+ and K- very similar! Lighter systems?

K-/K+ Ratio from SIS up to RHIC

Astonishing only at low incident energies!

K+ threshold at 1.58 AGeV

K- threshold at 2.5 AGeV

K- and K+ are linked

Au+Au and Ni+Ni 1.5 AGeV

A. Förster, F. Uhlig et al., KaoS PRL 91 (2003) 152301

dashed line: stat. ModelStep 1 NN -> Λ K+ NStep 2 Λ π -> K- N

K- and K+ are linked via strangeness exchange

„Law of mass action“

J. Cleymans, et al. PLB603(2004)

Strangeness Exchange

If equilibrium, then K- yield just proportional to the density of K+ and the density of pions!

K+ proportional to Λ! (associate production!)

Hence: K-/K+ ~ pion density!

Test of the Law of Mass Action J. Cleymans et al., PLB

κ = ([π] [Y])/([K-] [N]) [Y] ~ [K+]

Transport model calculations

repulsive K+N

attractive K-N

In-medium effects just cancel in the K- yield!

Strangeness Exchange at AGS?

AGS: L. Ahle et al., PLB 490J. Klay et al., PRC68

PLB603

T(K-) < T(K+) at 1 – 2 A GeV

EbeamAGeV

TM

eV

K+

K-

0

100

200

0 5 10 15 20

Canonical Statistical Model

J. Cleymans, HO, K. Redlich, PR C59 (1999) 1663

Ni+Ni

Expected Centrality Dependence (SM)

Pion density

n(π) = exp(-Eπ/T)

Strangeness is conserved!

Kaon density

NN N Λ K+

n(K) = exp(-EK/T)

[g V ∫ … exp[-(EΛ-µB)/T]

J. Cleymans, HO, K. Redlich,

PRC 60 (1999)

Thanks, Claudia! Qualitative agreement! Except for AGS!

Chemical Freeze Out

J. Cleymans and K. Redlich, PRL 81 (1998) 5284

S. Wheaton, canonical statistical model

Λ/π

Corr. Volume prop to Apart

Drastic change expected at AGS energies!

Depends on the size of the correlation volume!

Grand-canonical limit

Apart

Mu

ltip

licit

yR

ati

o-

6 AGeV

= 1.2 0.1

= 1.9 0.1

- = 2.5 0.3

/- = 0.7 0.1

-/ = 0.7 0.3

/- = 1.3 0.3

(a)

(b)

(c)

(d)

(e)

(f)

050

100150

0

10

0

0.1

0.2

0

0.05

0.1

0

0.01

0

0.001

0 50 100 150 200 250 300 350

AGS

Au+Au 6 A GeV

P. Chung et al.,

E895 Coll.

PRL 91(2003)

updated

SPS NA49 Coll.You have the choice!

0

0.1

0.2

0.3

0.4

0 100 200 300 400

<Nwound>

<K+

>/<

Nw

ou

nd>

CCSiSiSSPbPb

0

0.05

0.1

0.15

0.2

0 100 200 300 400

Npart

K+/

CCSiSiSSPbPb

C. Höhne, PhD thesis

Two serious problems:

(i) How to get Apart in a reliable way?

From measurements?

But what is Apart?

(ii) From the fraction of σ(Reac)? Then it depends on the chosen value!

Divide by pions? Not Bad! But are we sure that π/Apart is flat?

Better: Compare central collisions of different systems!

NA49 Data - 158 AGeV PRL …

Ingrid Kraus et al., to be published Corr. vol. NOT prop to Apart

Modification of the Stat. Model

• Instead of: strangeness undersaturation factor S Fit parameter

• Alternative: small clusters (RC) in fireball (R):

– Chemical equilibrium in subvolumes: canonical suppression

– RC free parameter R

RC

Model setting with RC

• RHIC : clusters still much smaller than fireball

Above RC ~ 2 fm, nearly grand-canonical !

Conclusions

• Centrality dependence only qualitative! Apart is ill-defined.

• Canonical description roughly okay!

• Periph. PbPb -- central light system??

• From system-size dependence:

Correlation volume NOT prop. to Apart

Various ideas!

Here: fitting the corr. vol.! Small Rc