Does Hadronization happen via Cluster formation?

J. Cleymans I. KrausH. Oeschler K. Redlich

SQM2008, Beijing, Oct.7th, 2008

Chemical Freeze Out

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

NA49 Data - 158 AGeV

Ingrid Kraus et al.,

Phys. Rev. C76 (2007) 064903Corr. vol. NOT prop to Apart

Canonical Suppression (SHM)

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)

Canonical Suppression

can./grand can.

Example:

T = 170 MeV

μB = 1 MeV

Values for LHC

ΔS=1ΔS=3

Three options for SHM calculations:

a) Canonical with R given by system size

b) Additionally strangeness suppression via γs

c) Canonical suppression is controlled by RC which can differ from the system size R (cluster!)

I. Kraus, J. Cleymans, H. O., K. Redlich,

System size: Phys. Rev. C76 (2007) 064903

Phys. Rev. C76 (2007) 064903

System size (and energy dep.) of cluster size

• A+A: clusters smaller than fireball

• RC not well defined for RC ≥ 2 fm because suppression vanishes

Pb+PbAu+Au

For heavy systems possibly the correlation volume extends over about 2-3 fm.

Then no canonical suppression can be observed in the particle ratios!

Same three options for pp collisions:

a) Canonical with R given by system size

b) Additionally strangeness suppression via γs

c) Canonical suppression is controlled by RC which can differ from the system size R (cluster!)

I. Kraus, J. Cleymans, H. O., K. Redlich,

pp: arXiv:0808:0611

T = 165 MeV, μB = 220 MeV

b) γS = 0.7

c) RC = 1.0 ± .3 fm, R = 1.4 fm

T = 165 MeV, μB = 14 MeV

b) γS ~ 1

c) RC ~ R = 1.3 fm

I. Kraus et al., arXiv:0808.0611

Extrapolation to LHC for pp

Predictions for pp at LHCPrediction for

heavy ions:

Grand can.

I. Kraus et al.,

PRC 74 (2007)

034903

I. Kraus, J. Cleymans, H. O., K. Redlich, arXiv:0808:0611

Predictions for T = 170 MeV and μB = 1 MeV

Most sensitive particle ratio for RC

Early decision on correlation volume!

STAR nucl-ex.0808.2041

Answer is a few months from ALICE!!!

Statistical Hadronization Model:

S = 0 -> no canonical suppression for ϕ

Strangeness undersaturation:

Suppression goes with (γs)ns with nS = 2

News on the ϕ Puzzle

J.H.Chen (STAR) QM2008,nucl-ex0804.4363

I. Kraus, et al., Phys.Rev. C76 (2007) 064903

S = 0R = 1

S = 2R as (K/π)2

ϕ/K- is rather constant with √s!

central collisions, heavy systems

Laura‘s talk yesterday, rise due to can. supp of K-

System-size dependence not explained as canonical effect,

if size prop. to Apart .

Cluster concept describes data! As well as γS does.

May be also in very heavy systems clusters,

as R above 2-3 fm grand-canonical behavior.

Cluster size in pp collisions R = 1 – 1.3 fm.

Does R increase with √s?

ϕ/K- always around 0.16, but higher at 1.7 AGeV (0.38±0.13)

In agreement with canonical description with s(ϕ) = 0

The ϕ Puzzle

• At high energies quark content seen,

but the effective strangeness content ?

• At low energies, SHM seems to work,