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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 3

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

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

Nucl. Phys. A 697 (2002) 902

Grand canonical ensemble

for Pb+Pb predictions

Thermal Parameters in Pb+Pb

hep-ph/0511094

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 5

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 6

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 7

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

_ _

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 8

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

_☺

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 9

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 10

T dependence: ratios with large mass differences

☺

• Ratios with larger mass

differences are more

sensitive

T from Ω and/or

ΩK

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

R

RC

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 12

System size and energy dependence of T and B

• T independent of– System size

– Data selection

– Energy • μB smaller at RHIC

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 13

System size and energy dependence of the cluster size

• p+p– energy dependence?

• Pb+Pb– depends on data selection

(multi-strange hadrons needed)

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 14

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 15

Canonical Suppression

• Particle ratios saturate

at RC ≈ 2 - 3 fm

– no precise determination

for small strangeness

suppression

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 16

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 17

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 18

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 19

Resonance Contribution to p/p

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

_

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 20

Resonance Contribution to K and

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 21

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 22

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

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 23

Fit Example

• All Fits were performed with

THERMUS

hep-ph/0407174

• Fits with S / RC give better

description of data

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 24

System size dependence of T and B

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

• …. as expected from increasing antibaryon / baryon ratio

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 25

System size dependence of the cluster size

Same trend as K /

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

More SPS and RHIC 200 GeV Data

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 27

Model setting with S

• S

– sensitive on data sample

– increase with size

– increase with energy

Ingrid Kraus, TU Darmstadt SQM 2006, UCLA, March 26, 2006 28

Prediction for p+p

• similar trend is seen in

S dependence