Strangeness and entropy

1
Strangeness and entropy
2
Centrality dependence
Solid STAR Au-Au vsNN 200 GeV Hollow - NA57
Pb-Pb vsNN 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
3
Centrality dependence
STAR Preliminary

• Use stat. model info
• C p-p
• Strangeness suppressed
• GC central A-A
• Strangeness saturated
• Transition describes
• E(i) behaviour
• T 170-165 MeV
• assume same T for p-p and Au-Au

Au-Au vsNN 200 GeV
K. Redlich
4
Centrality dependence
Correlation volume V (ANN) V0 ANN
Npart/2 V0 4/3 pR03 R0 1.1 fm
proton radius/ strong interactions
STAR Preliminary
T 170 MeV
T 165 MeV
Au-Au vsNN 200 GeV
Seems that T170 MeV fits data best but
shape not correct
K. Redlich
5
Varying T and R
Au-Au vsNN 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
K. Redlich
6
Npart dependence
Correlation volume V (ANN)a V0
ANN Npart/2 V0 4/3 pR03 R0 1.2
fm proton radius/ strong interactions
STAR Preliminary
T 165 MeV a 1/3
T 165 MeV a 1
T 165 MeV a 2/3
Au-Au vsNN 200 GeV
Seems to be a linear dependence on collision
geometry
K. Redlich
7
More on flavour dependence of E(i)
PHOBOS measured E(ch) for 200 and 19.6
GeV Enhancement for all particles?
PHOBOS Phys. Rev. C70, 021902(R) (2004)
Au-Au vsNN 200 GeV
Yes not predicted by model
Similar enhancement for one s hadrons
8
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
TDS DE
increase vs ? increase S
Blue Exp. fit Tc 158 MeV
r(m) (GeV-1)
Green - 1411 states of 1967 Red 4627 states of
1996
m (GeV)
9
Entropy and energy density

• Landau and Fermi (50s)
• Energy density, e, available for particle
  creation
• Assume S produced in early stages of collision
• Assume source thermalized and expands
  adiabatically
• Preserve S
• Ideal fluid
• S correlated to e via EOS

dNch/dh is correlated to S
10
Entropy and vs

• Approximate EOS for that of massless pions.
• Assume blackbody
• s S/V related to e

s
Fn(vs)
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Nch as measure of entropy
J.Klay Thesis 2001

• Entropy in Heavy Ion
• gt Entropy in p-p?

Different EOS? QGP?
12
Heavy-ion multiplicity scaling with vs
There is a scaling over several orders of
magnitude of v s
i.e. As function of entropy
PHOBOS White Paper Nucl. Phys. A 757, 28
13
HBT radii
No obvious trends as fn of vs
p HBT radii from different systems and at
different energies scale with (dNch/d?)1/3
power 1/3 gives approx. linear scale
Works for different mT ranges
Entropy determines radii
14
Eccentricity and low density limit
v2 different as fn Npart and energy

• At hydro. limit v2 saturates
• At low density limit

Apparent complete failure. Especially at low
density!
Voloshin, Poskanzer PLB 474 (2000) 27
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Fluctuations matter
PHOBOS QM2005
Important for all Cu-Cu and peripheral Au-Au
16
Now see scaling
Energy range scanned from vs 4-200 GeV
Again dN/dy i.e. entropy important
low density limit scaling now works
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Strangeness vs entropy
Solid STAR Au-Au vsNN 200 GeV Hollow - NA57
Pb-Pb vsNN 17.3 GeV
dNch/dh npp((1-x)Npart/2 xNbin) npp
Yield in pp 2.29 ( 1.27) x 0.13
No scaling between energies
But does become linear at higher dNch/dh
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LHC prediction I
6.4 RHICx1.6
Most central events dNch/dh 1200
PHOBOS White Paper Nucl. Phys. A 757, 28
19
LHC prediction II
Most central events dNch/dh 1200 dNch/dh1/3
10.5
Ro Rs Rl 6 fm
20
LHC prediction III
Most central events dNch/dh 1200 S 20
But I suspect Im not in the low density limit
any more so
v2/e 0.2
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LHC prediction IV
Most central events dNch/dh 1200
03
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Models readily available to experimentalists
Models 4 parameter Fit SHARE V1.2 THERMUS V2
Authors M. Kaneta et al. G. Torrieri, J. Rafelski et al. S. Wheaton and J. Cleymans
Ensemble Grand Canonical Grand Canonical Canonical and Grand Canonical
Parameters T, ?q, ?s , ?s T, ?q , ?s , ?s, ?q , ?I3, N, ?C , ?C 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 feed- down (harder to manipulate)
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First make a consistency check

• Require the models to, in principle, be the
  same.
• Only allow the least common multiple of
  parameters T, ?q, ?s, ?s
• Use Grand Canonical Ensemble.
• Fix weak feed-down estimates to be the same
  (i.e. at 100 or 0).

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The results
Au-Au vsNN 200 GeV
Ratio STAR Preliminary
p-/p K-/K ?p/p K-/p- ?p/p- L/p- ?L/p- X-/p- ?X/p- W/p- ?W/W 1.010.02 0.960.03 0.770.04 0.150.02 0.0820.009 0.0540.006 0.0410.005 (7.81) 10-3 (6.30.8) 10-3 (9.51) 10-4 1.010.08
after feed-down increase ?s decrease T
1 ? error
Similar T and ?s Significantly different errors.

Not identical and feed-down really matters
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Best predictions (with feed-down) 0-5
THERMUS THERMUS
??B 45 10 MeV
??S 22 7 MeV
??Q -21 8 MeV
T 168 6 MeV
?s 0.92 0.06
SHARE SHARE
?lq 1.05 0.05 (23 MeV)
ls 1.02 0.08 (5 MeV)
T 133 10 MeV
?s 2.03 0.6
?q 1.65 0.5

?s 1.07 0.2
Au-Au vsNN 200 GeV STAR Preliminary
Kaneta Kaneta
??B 8.0 2.2 MeV
??S -10.3 4.5 MeV
T 154 4 MeV
?s 1.05 7
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Predictions from statistical model
Behavior as expected
27
Comparison between p-p and Au-Au
Au-Au vsNN 200 GeV STAR Preliminary
p-p vs 200 GeV STAR Preliminary
Canonical ensemble
T 171 9 MeV
?s 0.53 0.04
r 3.49 0.97 fm
T 168 6 MeV
?s 0.92 0.06
r 15 10 fm
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Conclusions

• dNch/dh is strongly correlated with entropy
• dNch/dh scales as log(vs)
• 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