Statistical Model Predictions for p+p and Pb+Pb Collisions at LHC

Statistical Model Predictions for p+p and Pb+Pb Collisions at LHC

Ingrid Kraus

Nikhef and TU Darmstadt

Ingrid Kraus, Nikhef Heavy Ion Collisions School, Erice, Sept 18, 2008 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 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


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


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


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


T and μB dependence I: h / h ratios

• Sensitive on μB

determine μB from p/p

• weakly dep. on T

_

_☺


T dependence: ratios with large m

☺

• Ratios with larger mass

differences are more

sensitive

T from and/or

K


T and μB dependence II: mixed ratios

• Controlled by masses

• Weakly dep. on μB and T

• K/

– not usable for T and B

determination

– good test of predictions


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


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


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


System size and energy dep. of 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



• A+A: clusters smaller than fireball

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

RC

= R

Pb+PbAu+Au



• Particle ratios saturate at RC ≈ 2 - 3 fm

– no precise determination for weak strangeness suppression

Pb+PbAu+Au

RC

= R


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


System size and energy dep. of T and B

p+p C+C Si+Si Pb/Au

• T, μB weakly dependent on system size


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


Prediction for p+p

• significant increase of

ratios at RC ≈ 1.5 fm

• RC will be determined

with ALICE data


Extraction of RC

• Sensitivity increases

with strangeness

difference

RC from ☺hep-ph 0808.0611


• For Pb+Pb ratio was

proposed as a measure

of T but …

• Sensitivity on canonical

suppression is much

stronger than on T


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


Data and fits

Statistical Model Predictions for p+p and Pb+Pb Collisions at LHC

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