Transcript Slide 1

ENERGY AND SYSTEM SIZE
DEPENDENCE OF CHEMICAL
FREEZE-OUT
OUTLOOK
Statistical hadronization model
Data and analysis
Chemical 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:
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Large systems
In heavy ion collisions it is enought to take into account the conservation of
charges in the average sense (Grand-canonical ensemble)
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
The final multiplicity is the sum of primary production + particles coming
from resonance decays.
For most of the lightest members of hadronic families major contribution
comes from the decays.
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
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
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
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)
Jaakko Manninen
Phys.Rev.C73:044905,2006
STAR collaboration:
Phys. Rev. C70:041901,2004
Phys. Rev. Lett. 92:182301,2004
Phys. Lett. B595:143,2004
Nucl. Phys. A715:470,2003
nucl-ex/0311017
Phys. Rev. C66:061901,2002
Phys. Rev. Lett. 89:092302,2002
Phys. Rev. C65:041901,2002
nucl-ex/0606014
Phys. Rev. C71:064902,2005
Phys. Lett. B612:181,2005
Phys. Rev. Lett. 92:112301,2004
PHENIX collaboration:
Phys. Rev. Lett. 89:092302,2002
Phys. Rev. C69:024904,2004
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
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 AGeV
Kyield 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 parameters
More particles: lower temperature, higher S
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
NA49: p-p 158AGeV
prtcl
measurement
stat. model
+
3.15 +- 0.16
3.25
-
2.45 +- 0.12
2.43
+
0.21 +- 0.02
0.23
-
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
K0s
K
K


Exact canonical calculation
(B=Q=2, S=0)
Model with S does not describe
multistrange hyperons well !
use model in which mean number of
poissonially distributed strange quark
pairs hadronize
T
181.5 +- 3.4 MeV
hssi
0.46 +- 0.020
0.036
VT3
6.2 +- 0.5
0.18 +- 0.04
0.14
2/dof
(1520)
0.012 +- 0.003
0.011

0.012 +- 0.0015
0.020
Jaakko Manninen
8.4/10
 removed from the fit due to 5 deviation
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
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
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
STAR: Au-Au  sNN = 200 GeV (5% most central)
prtcl
measurement
stat. model
+
322 +- 32
325
-
327 +- 33
327
+
51.3 +- 7.7
57.1
T
161.0 +- 3.9 MeV
-
49.5 +- 7.4
53.5

1.02 +- 0.05
16.7 +- 1.1
16.0
S
anti 
12.7 +- 0.92
12.1
B
30.0 +- 9.8 MeV
2.17 +- 0.20
1.87
VT3e-
12.5 +- 0.7
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
K
K


-
+
Most of the rapidity densities are
described well with SHM
nucl-ex/0310004
0.7/T
2/dof
12.5/8
STAR:
T
157 +- 6 MeV
S
0.86 +- 0.11
B
22 +- 4 MeV
STAR: Au-Au  sNN = 130 GeV (5% most central)
prtcl
measurement
stat. model
+
239 +- 10.6
229
-
239 +- 10.6
232
+
47.6 +- 6.7
47.3
-
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
T
160.3 +- 4.4 MeV
p
26.7 +- 6.0
31.8
S
1.25 +- 0.08
anti p
19.1 +- 4.3
21.6

36.3 +- 12.7 MeV
6.09 +- 0.77
7.0
B
K0s
35.6 +- 5.7
45.9
VT3e-
8.2 +- 0.6
K(892)0
10.9 +- 2.7
13.6
K
K


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
0.7/T
2/dof
5.6/9
PHENIX: Au-Au  sNN = 130 GeV (5%)
prtcl
measurement
stat. model
+
276 +- 36
264
-
270 +- 35
270
+
46.7 +- 7.2
46.2
-
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
K
K
T
158.0 +- 5.9 MeV
S
1.24 +- 0.22
B
33.5 +- 17.8 MeV
VT3e-
8.1 +- 1.1
0.7/T
2/dof
0.5/4
Experimental data 5% most central
Consistency check:
A subset (without multistrange
hyperons) of the STAR 130 AGeV data
Fit to PHENIX data agrees with the
fit to STAR data
PHENIX: Au-Au  sNN = 130 GeV (5%)
prtcl
measurement
stat. model
S == 1
+
276 +- 36
264
280
-
270 +- 35
270
285
+
46.7 +- 7.2
46.2
42.0
-
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
K
K
T
S
B
VT3e0.7/T
2/dof
158.0 +- 5.9 MeV 158.0 +- 5.9 MeV
1.24 +- 0.22
1.00 (fixed)
33.5 +- 17.8 MeV 31.9 +- 17.1 MeV
8.1 +- 1.1
9.2 +- 0.6
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
(STAR
Cleymans et. al)
B= B (√sNN)
B(17.2 GeV) ≈ 250 MeV
Jaakko Manninen
NA49 √sNN = 17.2 GeV
C-C, Si-Si and Pb–Pb
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Energy dependence: Baryon chemical potential
Baryon chemical potential is a smooth,
strongly decreasing function of the
beam energy at AGS-SPS energy
regime
Energy dependence
can be parameterized as
B =  ln(√sNN) / (√sNN)
with
 ≈ 2.0 and
≈ 1.1
or Cleymans et al:
B = a/(1+√sNN/b)
with
a ≈ 1.3 GeV and
b ≈ 4.3 GeV
RHIC points are compatible with these
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Energy dependence: Baryon chemical potential
S scales with B
B ≈ 4.2 S
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Energy dependence: Temperature
At AGS-SPS energy regime
√sNN = 4 – 17
Strong energy dependence
T = a – bB2
T= T0(A) – C*B(√sNN)2
At heavy ion collisions
(A ¼ constant):
T = T0 – C*[ ln (√sNN) / √sNN]2
with
T0(208) = 162 MeV
C = b2 ≈ 0.67 and
 ≈ 1.13
RHIC points are compatible with
this
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
System size dependence: Temperature
At top SPS energy √sNN = 17.2
Small 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)
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Energy dependence: Strangeness equilibration
?
= 4 – 17 : S ≈ 0.7 – 0.9
Moderate energy dependence
√sNN
S = 1 – a exp (-b√[A√sNN])
a ≈ 0.61
b ≈ 0.021
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Energy dependence: Strangeness equilibration
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
System size dependence: Strangeness equilibration
Strong system size dependence
at top SPS beam energy
S = 1 – a exp (-b√[A√sNN])
From a fit without multistrange hyperons
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
System size dependence: Strangeness equilibration
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
Chemical freeze out
Line is T = a – b B2
Heavy ion systems fulfil E/N = 1GeV
Si –Si : E/N ≈1.1 GeV
C-C :
E/N ≈1.15 GeV
p-p:
E/N ≈1.2 GeV
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006
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
Jaakko Manninen
Critical Point and Onset of Deconfinement ; Firenze 5th of July 2006