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Statistical Model Predictions for p+p and Pb+Pb Collisions at LHC
Ingrid Kraus
Nikhef and TU Darmstadt
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 2
Outline
• Predictions for Pb+Pb collisions at LHC– Extrapolation of thermal parameters, predictions
– Experimental observables for T and μB determination
• From Pb+Pb to p+p: system size and energy dependence– Model ansatz with correlated, equilibrated clusters
– Analysed data and results
• Predictions for p+p collisions at LHC– Driven by initial or final state?
• Summary
• in Collaboration with H. Oeschler, K. Redlich, J. Cleymans, S. Wheaton
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 3
Hadron ratios in the grand canonical ensemble
• Grand canonical ensemble– large systems, large number of produced hadrons
– two parameters describe particle ratios in the hadronic final
state
A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl. Phys. A772 (2006) 167
T, V,
T, Vb, Nb
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 4
On the freeze-out curve:
TLHC ≈ TRHIC ≈ 170 MeV
T ≤ TC ≈ 170 MeV
μB from parametrised
freeze-out curve:
μB (√(sNN) = 5.5TeV) = 1 MeV
Phys. Rev. C 73 (2006) 034905
Grand canonical ensemble
for Pb+Pb predictions
Thermal Parameters in Pb+Pb
Phys. Rev. C 73(2006) 034905
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 5
Predictions for Pb+Pb
• Reliable for stable
particles
• Benchmark for
resonances
• Errors:
T = 170 +/- 5 MeV
μB = 1 + 4 MeV
Phys. Rev. C 74 (2006) 034903
- 1
All calculations with THERMUS hep-ph/0407174
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 6
T and μB dependence I: mixed ratios
• Controlled by masses
• Weakly dep. on μB and T
– μB term cancels
– larger contributions from
resonances at higher T
T
mm
Tm
m S expexp2/3
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 7
T and μB dependence I: mixed ratios
• Controlled by masses
• Weakly dep. on μB and T
– μB term cancels
– larger contributions from
resonances at higher T
T
mm
Tm
m S expexp2/3
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 8
T and μB dependence I: mixed ratios
• Controlled by masses
• Weakly dep. on μB and T
– μB term cancels
– larger contributions from
resonances at higher T
• K/
– not usable for T and B
determination
– good test of predictions
T
mm
Tm
m S expexp2/3
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 9
T and μB dependence II: h/h ratios
• Sensitive on μB
– μS opposite trend of μB
– determine μB from p/p
• weakly dep. on T
_
T
NN
h
h SSBB 2exp
_☺
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 10
T dependence: ratios with large mass differences
☺
• Ratios with larger mass
differences are more
sensitive
T from and/or
K
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 11
Canonical suppression
• Canonical ensemble– small systems / peripheral collisions,
low energies
– suppressed phase-space for particles
related to conserved charges
– Stronger suppression for multi-strange
hadrons
– Suppression depends on strangeness
content, not difference
)(
)(
0 xI
xInn Scanonicalgrandi
canonicali
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 12
Canonical suppression
• Canonical ensemble– small systems / peripheral collisions, low
energies
– suppressed phase-space for particles
related to conserved charges
– Stronger suppression for multi-strange
hadrons
– Suppression depends on strangeness
content, not difference
– Suppressed strangeness production
beyond canonical suppression
)(
)(
0 xI
xInn Scanonicalgrandi
canonicali
SPS √(sNN) = 17 AGeV
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 13
Modification of the model
• Statistical Model approach: T and μB
– Volume for yields → radius R used here
• Deviations: strangeness undersaturation factor S
– Fit parameter
• Alternative: small clusters (RC) in fireball (R): RC ≤ R
– Chemical equilibrium in subvolumes: canonical suppression
– RC free parameter
• Study – p+p, C+C, Si+Si, Pb+Pb / Au+Au collisions
– at SPS and RHIC energies
R
RC
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 14
System size and energy dependence of the cluster size
• Small clusters in all systems
• Small system size dependence
• p+p– energy dependence?
• Pb+Pb / Au+Au– data consistent with saturated
strangeness production
p+p C+C Si+Si Pb/Au
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 15
System size and energy dependence of the 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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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 16
System size and energy dependence of the cluster size
• Particle ratios saturate at RC ≈ 2 - 3 fm
– no precise determination for weak strangeness suppression
Pb+PbAu+Au
RC
= R
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 17
Extrapolation to LHC: T - B – systematics
• Chemical decoupling conditions
extracted from SIS up to RHIC
feature common behavior
• Extrapolation to LHC energy
with parametrisation e.g.
Nucl. Phys. A 697 (2002) 902
Phys. Rev. C 73(2006) 034905
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 18
System size and energy dependence of T and B
p+p C+C Si+Si Pb/Au
• T, μB weakly dependent on system size
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 19
Extrapolation to LHC: cluster size
• what defines RC in
p+p?
• initial size of p+p
system relevant
– RC const
• final state of large
number of produced
hadrons relevant
– RC increases with
multiplicity
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 20
Prediction for p+p
• significant increase of
ratios at RC ≈ 1.5 fm
• K / and
behave differently– multistrange hadrons
suffer stronger
suppression
• RC will be determined
with ALICE data
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 21
Extraction of RC
• Particle ratios w/o
strangeness are
insensitive to RC
• Sensitivity increases
with strangeness
difference
RC from ☺
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Ingrid Kraus, Nikhef Last call for predictions workshop, CERN, May 30, 2007 22
Summary
• Pb+Pb– predictions for particle ratios with
extrapolated parameters T, μB
– T, μB determination with p / p and
/ K or / ratios
_
• p+p– predictions difficult due to
unknown degree of canonical
suppression
– Cluster radius RC from data