Is soft physics entropy driven?

1
Is soft physics entropy driven?
Hot Quarks 2006
Outline

• Entropy and heavy-ions
• HBT radii
• Elliptic flow
• Strangeness
• LHC predictions

2
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)
3
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
4
Entropy and vs

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

s
Fn(vs)
5
Nch as measure of entropy
J.Klay Thesis 2001

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

Different EOS? QGP?
6
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
7
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
8
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
10
Now see scaling
Energy range scanned from vs 4-200 GeV
Again dN/dy i.e. entropy important
low density limit scaling now works
11
Strangeness production
Solid STAR Au-Au vsNN 200 GeV Hollow - NA57
Pb-Pb vsNN 17.3 GeV

• G C models
• linear increase with strangeness production
  volume
• Volume ? Npart
• Increase should decrease with vs

None of the predictions seem correct
STAR Preliminary
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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
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LHC prediction II
Most central events dNch/dh 1200 dNch/dh1/3
10.5
Ro Rs Rl 6 fm
15
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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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

Soft physics driven by entropy not Npart
18
Elliptic flow
v2 same for 200 62 GeV Au-Au at fixed pT
v2 decreases by 50 from RHIC to SPS
No perfect scaling but hints
v2 same in Au-Au and Cu-Cu for same centrality
19
Reminder
Entropy S
Classical thermodynamics A measure of the
amount of energy in a physical system that
cannot be used to do work.
Statistical thermodynamics A measure of the
statistical "mixedupness" of the thermodynamic
system The amount of uncertainty that would
remain about the exact microscopic state of the
system, given a description of its macroscopic
properties.
TDS DE
20
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
21
Can we describe vs dependence?
PHOBOS Phys. Rev. C70, 021902(R) (2004)
Theres a correlation between dNch/dh and Npart/2
small dotted lines are dNch/dh
npp(1-x)Npart/2 xNbin npp Yield in pp
2.29 ( 1.27) x 0.13
N.B. SPS energy only 17 GeV
If know npp can predict yield at any ?Npart?