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Does Hadronization happen via Cluster formation?
J. Cleymans I. KrausH. Oeschler K. Redlich
SQM2008, Beijing, Oct.7th, 2008
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Chemical Freeze Out
J. Cleymans and K. Redlich, PRL 81 (1998) 5284
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NA49 Data - 158 AGeV
Ingrid Kraus et al.,
Phys. Rev. C76 (2007) 064903Corr. vol. NOT prop to Apart
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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)
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Canonical Suppression
can./grand can.
Example:
T = 170 MeV
μB = 1 MeV
Values for LHC
ΔS=1ΔS=3
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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
R
RC
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Phys. Rev. C76 (2007) 064903
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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
RC
= R
Pb+PbAu+Au
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For heavy systems possibly the correlation volume extends over about 2-3 fm.
Then no canonical suppression can be observed in the particle ratios!
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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
R
RC
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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
p+p
I. Kraus et al., arXiv:0808.0611
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Extrapolation to LHC for pp
?
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Predictions for pp at LHCPrediction for
heavy ions:
Grand can.
I. Kraus et al.,
PRC 74 (2007)
034903
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I. Kraus, J. Cleymans, H. O., K. Redlich, arXiv:0808:0611
Predictions for T = 170 MeV and μB = 1 MeV
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Most sensitive particle ratio for RC
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Early decision on correlation volume!
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STAR nucl-ex.0808.2041
?
Answer is a few months from ALICE!!!
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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
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J.H.Chen (STAR) QM2008,nucl-ex0804.4363
S = 2
S =1
ϕ
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I. Kraus, et al., Phys.Rev. C76 (2007) 064903
S = 0R = 1
S = 2R as (K/π)2
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ϕ/K- is rather constant with √s!
central collisions, heavy systems
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Laura‘s talk yesterday, rise due to can. supp of K-
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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
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The ϕ Puzzle
• At high energies quark content seen,
but the effective strangeness content ?
• At low energies, SHM seems to work,
ignoring the s content of the ϕ but what is its justification?
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STAR Coll.,PRL 99 (2007)112301
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Partcile Production from SIS to the LHC
J. Cleymans, I. Kraus, H. Oeschler, K. Redlich
Does Hadronization happen via Cluster formation?
Beijing, Oct.7th, 2008
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STAR Coll. Phys. Rev. C 71 (2005) 064902
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RC is hardly increasing with system size!
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What is the strangeness content of the ϕ?
• Data from SPS centrality dependence in PbPb
• System size dependence pp, CC, SiSi
• Data from RHIC AuAu
• New results from 1 – 2 AGeV SIS