# Presentation: 854516

## Is soft physics entropy driven?

- Outline

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

- Hot Quarks 2006

## Hagedorn temperature (1965)

- Resonance mass spectrum grows exponentially
- Add energy to system produce more and more particles
- Maximum T for a system of hadrons.

- Blue – Exp. fit
- Tc= 158 MeV

- r(m) (GeV-1)

- Green - 1411 states of 1967
- Red – 4627 states of 1996

- m (GeV)

- TH ~ 160 MeV

- TS = E

-  increase √s  ↔ increase S

## Entropy and energy density

-  Landau and Fermi (50s)
-  Energy density,  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 via EOS
- 

- dNch/d is correlated to S

## Entropy and √s

-  Approximate EOS for that of massless pions.
-  Assume blackbody
-  s = S/V related to 

- s

- = Fn(√s)

## Nch as measure of entropy 

- Nch as measure of entropy

- Entropy in Heavy Ion
- > Entropy in p-p?

- J.Klay Thesis 2001

- Different EOS? QGP?

## Heavy-ion multiplicity scaling with √s

- PHOBOS White Paper: Nucl.  Phys. A 757, 28

- i.e. As function of entropy

- There is a scaling over several orders of magnitude of √ s

## HBT radii

- Entropy determines radii

- No obvious trends as fn of √s

-  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

## Eccentricity and low density limit

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

- Apparent complete failure.
- Especially at low density!

- Voloshin, Poskanzer PLB 474 (2000) 27

- v2 different as fn Npart and energy

## Fluctuations matter

- Important for all Cu-Cu and peripheral Au-Au

- PHOBOS
-  QM2005

## Now see scaling

- Again dN/dy i.e. entropy important

- Energy range scanned from
- √s= 4-200 GeV

## Strangeness production

- STAR Preliminary

-  G C models –
- linear increase with  strangeness production volume
-       Volume  Npart
-  Increase should decrease with √s

- Solid –   STAR Au-Au √sNN = 200 GeV
- Hollow - NA57 Pb-Pb √sNN = 17.3 GeV

- None of the predictions seem correct

## Strangeness vs entropy

- Solid –   STAR Au-Au √sNN = 200 GeV
- Hollow - NA57 Pb-Pb √sNN = 17.3 GeV

- No scaling between energies

- But does become ~linear at higher dNch/d

- dNch/dnpp((1-x)Npart/2
- 			   + xNbin)
- npp= Yield in pp
-      = 2.29 ( 1.27)
- x = 0.13

## LHC prediction I

- PHOBOS White Paper: Nucl.  Phys. A 757, 28

**6.4 = RHICx1.6**

- Most central events:
- dNch/d ~1200

## LHC prediction II

- Ro = Rs = Rl = 6 fm

- Most central events:
- dNch/d ~1200
- dNch/d ~10.5

## LHC prediction III

- Most central events:
- dNch/d ~1200
- S ~ 20

- But I suspect I’m not in the low density limit any more so

- v2/ ~ 0.2

## LHC prediction IV

- Most central events:
- dNch/d ~1200

- 03

## Conclusions

-  dNch/dis strongly correlated with 	entropy
-  dNch/dscales as log(√s)
-  Several variables from the soft sector 	scale with dNch/d
-  HBT
-  v2 at low densities
-  Strangeness centrality dependence

- Soft physics driven by entropy not Npart

## Elliptic flow

- v2 decreases by ~ 50% from RHIC to SPS

- v2 same for 200 – 62 GeV Au-Au at fixed pT

- v2 same in Au-Au and Cu-Cu for same centrality

- No perfect scaling but hints

## Reminder

- TS = E

- Entropy  = S

- 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.

- Classical thermodynamics –
- 	A measure of the amount of energy in a physical system 		that cannot be used to do work.

## HBT radii

- Entropy determines radii

- No obvious trends as fn of √s

-  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

- Can we describe √s dependence?

- N.B.: SPS energy only 17 GeV

- There’s a correlation between dNch/d and Npart/2

- If know npp can predict yield at any Npart

- small dotted lines are:
- dNch/dnpp(1-x)Npart/2 + xNbin
- npp= Yield in pp
-      = 2.29 ( 1.27)
- x = 0.13