Strangeness and entropy
Helen Caines
Yale University
Strasbourg - May 2006
Centrality dependence
Solid – STAR Au-Au √sNN = 200 GeV
Hollow - NA57 Pb-Pb √sNN = 17.3 GeV
STAR Preliminary
We can describe p-p
and central Au-Au average
ratios.
Can we detail the
centrality evolution?
Look at the particle
enhancements.
E(i) = YieldAA/Npart
Yieldpp /2
Helen Caines
Strasbourg – May 2006
2
Centrality dependence
STAR Preliminary
• Use stat. model info:
C – p-p
Strangeness suppressed
GC – central A-A
Strangeness saturated
• Transition describes
E(i) behaviour
Au-Au √sNN = 200 GeV
• T =170-165 MeV
assume same T for p-p and Au-Au
K. Redlich
Helen Caines
Strasbourg – May 2006
3
Centrality dependence
Correlation volume:
STAR Preliminary
V= (ANN) ·V0
ANN = Npart/2
V0 = 4/3 p·R03
R0 = 1.1 fm
proton radius/
strong interactions
T = 165
170 MeV
Au-Au √sNN = 200 GeV
Seems that T=170 MeV fits data best
– but shape not correct
K. Redlich
Helen Caines
Strasbourg – May 2006
4
Varying T and R
Au-Au √sNN = 200 GeV
Calculation for most
central Au-Au data
Correlation volume:
V0  R03
R0 ~ proton radius
strong interactions
Rapid increase in E(i) as T decreases
SPS data indicated R = 1.1 fm
Helen Caines
Strasbourg – May 2006
K. Redlich
5
Npart dependence
Correlation volume:
STAR Preliminary
V= (ANN)a ·V0
ANN = Npart/2
V0 = 4/3 p·R03
R0 = 1.2 fm
proton radius/
strong interactions
T = 165 MeV
1/3
a=1
2/3
Au-Au √sNN = 200 GeV
Seems to be a “linear” dependence on collision geometry
Helen Caines
Strasbourg – May 2006
K. Redlich
6
More on flavour dependence of E(i)
PHOBOS: Phys. Rev. C70, 021902(R) (2004)
PHOBOS:
STAR Preliminary
Au-Au √sNN = 200 GeV
measured E(ch)
for 200 and 19.6 GeV
Enhancement for all
particles?
Yes – not predicted by
model
Similar enhancement
for one s hadrons
Helen Caines
Strasbourg – May 2006
7
Hagedorn temperature (1965)
– Resonance mass spectrum grows exponentially
– Add energy to system produce more and more particles
– Maximum T for a system of hadrons. TH ~ 160 MeV
r(m) (GeV-1)
TDS = DE
increase √s ↔ increase S
Blue – Exp. fit
Tc= 158 MeV
Green - 1411 states of 1967
Red – 4627 states of 1996
filled: AA
open: elementary
m (GeV)
Helen Caines
Strasbourg – May 2006
[Satz: Nucl.Phys. A715 (2003) 3c
8
Entropy and energy density
• Landau and Fermi (50s)
• Energy density, e, available for particle creation
E ( sNN  2mN ) sNN
• ε 
V
2mN V0
• Assume S produced in early stages of collision
• Assume source thermalized and expands adiabatically
• Preserve S
• Ideal fluid
• S correlated to e via EOS
Helen Caines
dNch/dh is correlated to S
Strasbourg – May 2006
9
Entropy and √s
• Approximate EOS for that of massless pions.
1
p ε
3
• Assume blackbody
ε  T4
• s = S/V related to e
Ts ~ ε  p
s ~ ε 3/4
s
~
V( sNN  2mN )3/4
sNN
Helen Caines
1/4
Strasbourg – May 2006
= Fn(√s)
10
Nch as measure of entropy
J.Klay Thesis 2001
S
~ ε 3/4
V
( sNN  2mN )3/4
F
1/4
sNN
π
S
~
~F
V Np
Entropy in Heavy Ion
> Entropy in p-p?
Different EOS? QGP?
Helen Caines
Strasbourg – May 2006
11
Heavy-ion multiplicity scaling with √s
dNch /dη
 log( s )
Npart /2
There is a scaling over
several orders of
magnitude of √ s
i.e. As function of entropy
PHOBOS White Paper: Nucl. Phys. A 757, 28
Helen Caines
Strasbourg – May 2006
12
HBT radii
<kT>≈ 400 MeV (RHIC)
<kT>≈ 390 MeV (SPS)
No obvious trends as fn of √s
p HBT radii from
different systems and at
different energies scale
with (dNch/dη)1/3
power 1/3 gives approx.
linear scale
Works for different mT ranges
Entropy determines radii
nucl-ex/0505014 Lisa et al.
Helen Caines
Strasbourg – May 2006
13
Eccentricity and low density limit
v2 different as fn Npart
and energy
At hydro. limit v2
saturates
At low density limit
1 dN
v2 
eccent
Area dy
R2x  R2y
PHENIX preliminary
eccent 
R R
2
x
2
y
Voloshin, Poskanzer PLB 474 (2000) 27
Helen Caines
Apparent complete failure.
Especially at low density!
Strasbourg – May 2006
14
Fluctuations matter
PHOBOS
QM2005
Important for all Cu-Cu and peripheral Au-Au
Helen Caines
Strasbourg – May 2006
15
Now see scaling
Energy range
scanned from
√s= 4-200 GeV
Again dN/dy i.e.
“low density limit” scaling now works entropy important
Helen Caines
Strasbourg – May 2006
16
Strangeness vs entropy
dNch/dh  npp((1-x)Npart/2
+ xNbin)
Solid – STAR Au-Au √sNN = 200 GeV
Hollow - NA57 Pb-Pb √sNN = 17.3 GeV
npp= Yield in pp
= 2.29 ( 1.27)
x = 0.13
No scaling between
energies
But does become
~linear at higher
dNch/dh
Helen Caines
L
X
Strasbourg – May 2006
W
17
LHC prediction I
6.4 = RHICx1.6
6
5
Most central
events:
dNch/dh ~1200
5.5 TeV
1000
PHOBOS White Paper: Nucl. Phys. A 757, 28
Helen Caines
Strasbourg – May 2006
18
LHC prediction II
Most central events:
dNch/dh ~1200
dNch/dh1/3 ~10.5
Ro = Rs = Rl = 6 fm
Helen Caines
Strasbourg – May 2006
19
LHC prediction III
Most central events:
dNch/dh ~1200
S ~ 20
Helen Caines
But I suspect I’m not in the low
density limit any more so
v2/e ~ 0.2
Strasbourg – May 2006
20
LHC prediction IV
Most central events:
dNch/dh ~1200
dNL/dy = dNL/dy
~20-30
dNX/dy = dNX/dy
~4-6
dNW/dy = dNW/dy
~0.5-1
L
X
W
L
X
W
03
Helen Caines
Strasbourg – May 2006
21
Models readily available to experimentalists
Models
4 parameter
Fit
Authors
M. Kaneta et
al.
Ensemble Grand
Canonical
Parameters T, q, s , s
SHARE V1.2
THERMUS V2
G. Torrieri, J.
Rafelski et al.
Grand
Canonical
T, q , s , s, q
, I3, N, C , C
S. Wheaton and
J. Cleymans
Canonical and
Grand Canonical
T, B, S, Q, s, R
T, B, S , q, C,
s , C , R
Feed Down possible
default is with
% feed-down
default is no feeddown (harder to
manipulate)
Helen Caines
Strasbourg – May 2006
22
First make a consistency check
Helen Caines
Strasbourg – May 2006
23
The results
Ratio
p/p
K/K
p/p
K/p
p/p
L/p
L/p
X/p
X/p
W/p
W/W
Helen Caines
Au-Au √sNN = 200 GeV
STAR
Preliminary
after feed-down
1.01±0.02
increase s
0.96±0.03
decrease T
0.77±0.04
0.15±0.02
0.082±0.009
0.054±0.006
1  error
0.041±0.005
(7.8±1) 10-3
Similar T and s
-3
(6.3±0.8) 10
Significantly different errors.
(9.5±1) 10-4
Not identical and feed-down really matters
1.01±0.08
Strasbourg – May 2006
24
“Best” predictions (with feed-down) 0-5%
THERMUS
45 ± 10 MeV
S
22 ± 7 MeV
Q
-21 ± 8 MeV
T
168 ± 6 MeV
s
0.92 ± 0.06
SHARE
Au-Au √sNN = 200 GeV
STAR Preliminary
Helen Caines
B
Strasbourg – May 2006
q
1.05 ± 0.05 (23 MeV)
s
1.02 ± 0.08 (5 MeV)
T
133 ± 10 MeV
s
2.03 ± 0.6
q
1.65 ± 0.5
s
B
Kaneta
1.07
8.0 ±±0.2
2.2 MeV
S
-10.3 ± 4.5 MeV
T
154 ± 4 MeV
s
1.05 ± 7
25
Predictions from statistical model
B  nB  V
V  B / nB
 N part e  B / T
L  nL V
L  nL  V
 (e
e
B /T
S /T
e
S /T
 N part
)  N part e
B /T
 (e   B / T  e   S / T )  N part e  B / T
e
2 B / T
e
S / T
 N part
L  N partBehavior as expected
L  e  2  B / T  N part
Helen Caines
Strasbourg – May 2006
26
Comparison between p-p and Au-Au
Au-Au √sNN = 200 GeV
STAR Preliminary
p-p √s = 200 GeV
STAR Preliminary
Canonical ensemble
T
171 ± 9 MeV
T 168 ± 6 MeV
s 0.53 ± 0.04
r
Helen Caines
s 0.92 ± 0.06
3.49 ± 0.97 fm
r
Strasbourg – May 2006
15 ± 10 fm
27
Conclusions
• dNch/dh is strongly correlated with entropy
• dNch/dh scales as log(√s)
• Several variables from the soft sector scale with
dNch/dh
• HBT
• v2 at low densities
• Strangeness centrality dependence
• Statistical models
• Currently differences between models
• All get approximately the same results
• Also predict little change in strangeness at LHC
Soft physics driven by entropy not Npart
Helen Caines
Strasbourg – May 2006
28