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

Ingrid Kraus

Nikhef and TU Darmstadt

Ingrid Kraus, Nikhef QGP workshop, 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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 6

T and μB dependence I: h / h ratios

• Sensitive on μB

determine μB from p/p

• weakly dep. on T

_

_☺

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 7

T dependence: ratios with large m

☺

• Ratios with larger mass

differences are more

sensitive

T from and/or

K

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 8

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 9

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 10

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 11

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 12

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 13

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 14

System size and energy dep. of cluster size

• Particle ratios saturate at RC ≈ 2 - 3 fm

– no precise determination for weak strangeness suppression

Pb+PbAu+Au

RC

= R

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 15

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 16

System size and energy dep. of T and B

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

• T, μB weakly dependent on system size

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 17

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 18

Prediction for p+p

• significant increase of

ratios at RC ≈ 1.5 fm

• RC will be determined

with ALICE data

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 19

Extraction of RC

• Sensitivity increases

with strangeness

difference

RC from ☺hep-ph 0808.0611

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 20

• For Pb+Pb ratio was

proposed as a measure

of T but …

• Sensitivity on canonical

suppression is much

stronger than on T

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 21

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

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 22

Data and fits

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 23

Data and fits II

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 24

Tables from paper

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 25

Resonance Contribution to p/p

• Ratio not affected by feeding– net baryon number is conserved

_

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 26

Resonance Contribution to K and

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 27

Resonance Decays

• no resonance contribution

• – 50% from feed-down

– both exhibit same T dependence

• K decay exceeds thermal at LHC

• – thermal production ≈ constant

– resonance contribution dominant

• 75% of all from resonances

• p/pprimary ≈ p/pdecay

_ _

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 28

Sensitivity on T

• Thermal– K / and / have

same T dependence

– sensitivity increases

with mass difference

• Decay contribution– lighter particles are

stronger affected

– increasing feed-down

with increasing T

Relative variation of R per 1MeV change of T

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 29

More SPS and RHIC 200 GeV Data

Ingrid Kraus, Nikhef QGP workshop, Erice, Sept 18, 2008 30

Model setting with S

• S

– sensitive on data sample

– increase with size

– increase with energy