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

TU Darmstadt

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 2

Outline

• Predictions for Pb+Pb– Extrapolation of thermal parameters, predictions

– Experimental observables for T and μB determination

• From Pb+Pb to p+p: Model ansatz with correlated

clusters

• Predictions for p+p– Driven by initial or final state?

• Summary

• in Collaboration with H. Oeschler, K. Redlich, J. Cleymans, S. Wheaton


Comparison to Experimental Data

– Different data selected for fits

– Accurancy in T, B: few MeV

A.Andonic, P. Braun-Munzinger, J. Stachel, nucl-th/0511071


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

Nucl. Phys. A 697 (2002) 902

Grand canonical ensemble

for Pb+Pb predictions

Thermal Parameters in Pb+Pb

hep-ph/0511094


Predictions for Pb+Pb

• Reliable for stable particles

• Benchmark for resonances

• Errors:

T = 170 +/- 5 MeV

μB = 1 + 4 MeV

- 1

All calculations with THERMUS hep-ph/0407174


Analytical check

•

•

• Off by factor 2!

• Particle yield = thermal production

+ feed-down contributions

988.01701)1(222 ,,

==≈⋅−⋅+MeVMeV

TNN

eepp SpSBpB

36.01321

1672

2

4 170

351

17027.0)23(1)11(2/3

)()(2/3 ,,,,

=⋅⎟⎠⎞

⎜⎝⎛=

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛≈

ΞΩ

−⋅+−+⋅−

−−−+−

Ξ

Ω

Ξ

Ω−

− ΞΩΞΩΞΩ

MeV

MeV

MeVMeVMeV

Tmm

TNNNN

eeMeVMeV

eemm

gg SSSBBB

4)102(12

32

2)102(12

12

)12()12(

=+⋅⋅⎟⎠⎞

⎜⎝⎛ +=

=+⋅⋅⎟⎠⎞

⎜⎝⎛ +=

+⋅+=

Ω

Ξ

g

g

IJg

∑ →Γ+=j

thermaljij

thermalii NNN


Resonance Decays

• Ω no resonance contribution

• Ξ– 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

_ _


T and μB dependence I: 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 μμ2exp

_☺


T and μB dependence II: 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

⎥⎦⎤

⎢⎣⎡ −−⋅⎥⎦

⎤⎢⎣⎡−⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛∝

ΞΩ ΞΩ

Ξ

Ω−

−

T

mm

Tm

m S expexp2/3

μ


T dependence: ratios with large mass differences

☺

• Ratios with larger mass

differences are more

sensitive

T from Ω and/or

ΩK


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

R

RC


System size and energy dependence of T and B

• T independent of– System size

– Data selection

– Energy • μB smaller at RHIC


System size and energy dependence of the cluster size

• p+p– energy dependence?

• Pb+Pb– depends on data selection

(multi-strange hadrons needed)


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


Canonical Suppression

• Particle ratios saturate

at RC ≈ 2 - 3 fm

– no precise determination

for small strangeness

suppression


Extrapolation to LHC

• 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

• K / and ΩΞ

behave differently– multistrange hadrons

suffer stronger

suppression

• RC will be determined

with ALICE data


Summary

• Pb+Pb– predictions for particle ratios with

extrapolated parameters T, μB

– T, μB determination with p / p and

Ω/ K or Ω/ ratios

_

• p+p– predictions difficult due to

unknown degree of canonical

suppression

– Cluster radius RC from data


Resonance Contribution to p/p

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

_


Resonance Contribution to K and


Sensitivity on T

• Thermal– K / and Ω/ Ξ 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


Data Set

• Selection: + / - K+ / K- / K- / - / K+ / K- -

same for p+p C+C Si+Si Pb+Pb 4

and C+C Si+Si Pb+Pb mid rapidity

@ 158 A

GeV

• Compare different model settings

– Equilibrium: parameters T, μB, R

– Fit S : parameters S, T, μB, R

– Fit RC: parameters RC, T, μB, R


Fit Example

• All Fits were performed with

THERMUS

hep-ph/0407174

• Fits with S / RC give better

description of data


System size dependence of T and B

• μB decreases at mid-rapidity in small systems ….

• …. as expected from increasing antibaryon / baryon ratio


System size dependence of the cluster size

Same trend as K /


More SPS and RHIC 200 GeV Data


Model setting with S

• S

– sensitive on data sample

– increase with size

– increase with energy


Prediction for p+p

• similar trend is seen in

S dependence

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

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