ENERGY AND SYSTEM SIZE DEPENDENCE OF CHEMICAL FREEZE-OUT

ENERGY AND SYSTEM SIZE DEPENDENCE OF CHEMICAL FREEZE-

OUT

OUTLOOKStatistical hadronization model

Data and analysisChemical freeze out parameters

Jaakko Manninen Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006

Small systems


In small systems up to B~10, take into account only the charge configurations that match exactly the original net charge numbers (elementary systems)No chemical potentials, only 3 free parameters: T, V, S

For semi large systems, conserve strangeness exactly and introduce chemical potentials for B and Q (C-C and Si-Si)free parameters are: T, V, S, B and Q

Primary multiplicity:

Large systems

In heavy ion collisions it is enought to take into account the conservation of

charges in the average sense (Grand-canonical ensemble)


The final multiplicity is the sum of primary production + particles comingfrom resonance decays. For most of the lightest members of hadronic families major contribution comes from the decays.

6 free parameters: T,V, B, S, Q and S S and Q are fixed by additional conditions: Q/B = Z/A and S=0

Homogenious freeze out

Analysis may be performed assuming a single fireball, if

1) Distribution of charges and masses is the same as coming from random splitting of a single fireball and the sum of the rest frame volumes equals the volume of the large fireball.

2) The clusters are large and the distribution of charges, masses and

relevant thermal parameters is relatively flat (Boost invariant scenario).


#2 does not hold at SPS and below. #1 might hold at SPS, but 4 multiplicities must be taken into account.#2 might hold at RHIC since the rapidity distributions of pions and anti

baryon/baryon –ratios are flat at least in one unit of rapidity around y=0. The flat area is wider than a typical width of rapidity distribution coming from a single cluster at kinetic freeze out Allows to determine the characteristics of the average source at midrapidity

Data


experiment system beam energy

NA49 p-p 158 AGeV

NA49 C-C 158 AGeV

NA49 Si-Si 158 AGeV

NA49 Pb-Pb 158 AGeV

NA49 Pb-Pb 80 AGeV

NA49 Pb-Pb 40 AGeV

NA49 Pb-Pb 30 AGeV

NA49 Pb-Pb 20 AGeV

E-802 Au-Au 11.6 AGeV

STAR Au-Au 130 AGeV (CM)

PHENIX Au-Au 130 AGeV (CM)

STAR Au-Au 200 AGeV (CM)

Phys.Rev.C73:044905,2006

STAR collaboration:Phys. Rev. C70:041901,2004Phys. Rev. Lett. 92:182301,2004Phys. Lett. B595:143,2004Nucl. Phys. A715:470,2003nucl-ex/0311017Phys. Rev. C66:061901,2002Phys. Rev. Lett. 89:092302,2002Phys. Rev. C65:041901,2002nucl-ex/0606014Phys. Rev. C71:064902,2005Phys. Lett. B612:181,2005Phys. Rev. Lett. 92:112301,2004

PHENIX collaboration:Phys. Rev. Lett. 89:092302,2002Phys. Rev. C69:024904,2004

Pb – Pb collisions

In Pb-Pb systems most of the particle multiplicities are described well with SHM

Largest deviations from the experimental numbers: yield too large at all energies except 80 AGeV K+ yield too low at all energies except 158 AGeVK- yield too large gets worse as beam energy increases

However, some of the particle ratios are not described well at all

drops down at higher energies and agrees with RHIC ratio


Also, multiplicites at C-C and Si-Si are described well with SHM

Again, largest deviations from the experimental numbers are with

Possible sources for the deviations- The tail of the exponential mass spectrum gets more important at

high temperature- Distribution of charges among clusters is not equal to the one

coming from random splitting of a large cluster- Some reaction meachanisms are not taken into account

Statistical model results are not sensitive to other ’’internal variables’’ like widths and branching ratios.

Number of resonances included in the analysis can cause a shift in parametersMore particles: lower temperature, higher S

NA49: p-p 158AGeV

prtcl measurement stat. model

+ 3.15 +- 0.16 3.25

- 2.45 +- 0.12 2.43

K+ 0.21 +- 0.02 0.23

K- 0.13 +- 0.013 0.12

0.115 +- 0.012 0.133

anti 0.0148 +- 0.0019 0.0147

- 0.0031 +- 0.0003 0.0029

+ (9.2 +- 0.09) £ 10-4 9.18 £ 10-4

(2.6 +- 1.3) £ 10-4 8.87 £ 10-5

anti (1.6 +- 0.9) £ 10-4 6.16 £ 10-5

anti p 0.040 +- 0.007 0.036

K0s 0.18 +- 0.04 0.14

0.012 +- 0.003 0.011

0.012 +- 0.0015 0.020Jaakko Manninen Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006

Exact canonical calculation (B=Q=2, S=0)

removed from the fit due to 5 deviation

T 181.5 +- 3.4 MeV

hssi 0.46 +- 0.020

VT3 6.2 +- 0.5

2/dof 8.4/10

Model with S does not describe multistrange hyperons well !use model in which mean number of poissonially distributed strange quark pairs hadronize

Statistical approach at midrapidity

At RHIC statistical analysis may be performed in a limited rapidity window.

Similarly to 4 analysis, assume vanishing net strangeness. This is not quaranteed at midrapidity, but seems like a reasonable assumption (fixes S).

Take Q/B = Z/A (fixes Q).

Fit to the rapidity densities around y=0, i.e. scale particle densities with common scaling parameter V.

BRAHMS 4 data not suitable for statistical analysis without additional assumptions


STAR: Au-Au sNN = 200 GeV (5% most central)


+ 322 +- 32 325

- 327 +- 33 327

K+ 51.3 +- 7.7 57.1

K- 49.5 +- 7.4 53.5

16.7 +- 1.1 16.0

anti 12.7 +- 0.92 12.1

- 2.17 +- 0.20 1.87

+ 1.83 +- 0.21 1.53

anti

0.53 +- 0.057 0.63

p 34.7 +- 6.2 42.9

anti p 26.7 +- 4.0 30.9

7.70 +- 0.90 7.10

Most of the rapidity densities are described well with SHM

T 161.0 +- 3.9 MeV

S 1.02 +- 0.05

B 30.0 +- 9.8 MeV

VT3e-0.7/T 12.5 +- 0.7

2/dof 12.5/8

T 157 +- 6 MeV

S 0.86 +- 0.11

B 22 +- 4 MeV

STAR:

nucl-ex/0310004

STAR: Au-Au sNN = 130 GeV (5% most central)


+ 239 +- 10.6 229

- 239 +- 10.6 232

K+ 47.6 +- 6.7 47.3

K- 43.2 +- 6.0 43.6

17.2 +- 1.8 17.2

anti 12.2 +- 1.3 12.5

- 2.13 +- 0.27 1.87

+ 1.78 +- 0.24 1.47

0.34 +- 0.10 0.40

anti 0.36 +- 0.11 0.35

p 26.7 +- 6.0 31.8

anti p 19.1 +- 4.3 21.6

6.09 +- 0.77 7.0

0s 35.6 +- 5.7 45.9

K(892)0 10.9 +- 2.7 13.6

T 160.3 +- 4.4 MeV

S 1.25 +- 0.08

B 36.3 +- 12.7 MeV

VT3e-0.7/T 8.2 +- 0.6

2/dof 5.6/9

Experimental data centralitites: pions and Lambdas 5%K:s and p:s 6%Xi:s and Omega:s 10%phi 11%Everything extrapolated to 5% most central events by assuming linear scaling with dh-/dy

PHENIX: Au-Au sNN = 130 GeV (5%)


+ 276 +- 36 264

- 270 +- 35 270

K+ 46.7 +- 7.2 46.2

K- 40.5 +- 6.5 42.9

17.3 +- 4.4 15.9

anti 12.7 +- 3.4 11.8

p 28.7 +- 4.1 29.6

anti p 20.1 +- 3.0 20.6

T 158.0 +- 5.9 MeV

S 1.24 +- 0.22

B 33.5 +- 17.8 MeV

VT3e-0.7/T 8.1 +- 1.1

2/dof 0.5/4

Experimental data 5% most central

Fit to PHENIX data agrees with the fit to STAR data

Consistency check:A subset (without multistrange hyperons) of the STAR 130 AGeV data

PHENIX: Au-Au sNN = 130 GeV (5%)

prtcl measurement stat. model S == 1

+ 276 +- 36 264 280

- 270 +- 35 270 285

K+ 46.7 +- 7.2 46.2 42.0

K- 40.5 +- 6.5 42.9 39.2

17.3 +- 4.4 15.9 13.9

anti 12.7 +- 3.4 11.8 10.4

p 28.7 +- 4.1 29.6 30.3

anti p 20.1 +- 3.0 20.6 21.2

T 158.0 +- 5.9 MeV

158.0 +- 5.9 MeV

S 1.24 +- 0.22 1.00 (fixed)

B 33.5 +- 17.8 MeV

31.9 +- 17.1 MeV

VT3e-0.7/T 8.1 +- 1.1 9.2 +- 0.6

2/dof 0.5/4 2.0/5

The minima is quite flat:

Setting S == 1 describes

the data well

Setting S == 1 with STAR data (including

s and s)leads to worse fit with higher T

System size dependence: Baryon chemical potential


Baryon chemical potential seems to be independent on system size at 158AGeV

Centrality independence of B seen at √sNN = 200 and 17.2 GeV

NA49 √sNN = 17.2 GeVC-C, Si-Si and Pb–Pb

B= B (√sNN)B(17.2 GeV) ≈ 250 MeV

(STAR Cleymans et. al)

Energy dependence: Baryon chemical potential


Baryon chemical potential is a smooth, strongly decreasing function of the beam energy at AGS-SPS energy regime

Energy dependencecan be parameterized asB = ln(√sNN) / (√sNN)

with≈ 2.0 and≈ 1.1

or Cleymans et al:B = a/(1+√sNN/b)witha ≈ 1.3 GeV andb ≈ 4.3 GeV

RHIC points are compatible with these

Energy dependence: Baryon chemical potential


B ≈ 4.2 S

S scales with B

Energy dependence: Temperature


At AGS-SPS energy regime√sNN = 4 – 17Strong energy dependence

T = a – bB2

T= T0(A) – C*B√sNN)2

At heavy ion collisions(A ¼ constant): T = T0 – C*[ ln (√sNN) / √sNN

]2

withT0(208) = 162 MeVC = b2 ≈ 0.67 and≈ 1.13RHIC points are compatible with this

System size dependence: Temperature


At top SPS energy √sNN = 17.2Small systems decouple at higher temperature

T= T0(A) – C*B√sNN)2

A dependent T0 can be approximated logarithmically:

T0(A) = Tc – log(A) = 191.5 MeV – 4.5 MeV * log(A)

Energy dependence: Strangeness equilibration


√sNN = 4 – 17 : S ≈ 0.7 – 0.9Moderate energy dependence

S = 1 – a exp (-b√[A√sNN])

a ≈ 0.61b ≈ 0.021

?

Energy dependence: Strangeness equilibration


System size dependence: Strangeness equilibration


Strong system size dependenceat top SPS beam energy

S = 1 – a exp (-b√[A√sNN])

From a fit without multistrange hyperons

System size dependence: Strangeness equilibration


Chemical freeze out


Line is T = a – b B2

Heavy ion systems fulfil E/N = 1GeV

Si –Si : E/N ≈1.1 GeVC-C : E/N ≈1.15 GeVp-p: E/N ≈1.2 GeV

Summary


Statistical hadronization model describes vast variety of systems

Some details are not reproduced

Strangeness equilibrated only at RHIC

Model parameters are smooth functions of beam energy and system size allows phenomenological studies and predictions

ENERGY AND SYSTEM SIZE DEPENDENCE OF CHEMICAL FREEZE-OUT

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