1. Volume effects on strangeness production
“It isn’t size that counts so much as the way things are arranged.”
E.M. Forster (1879–1970)

2. Outline Introduction. What’s observed at lower energies.
Enhancement at RHIC?
pT dependence of strangeness production.
Is there a scaling in A-A production?
Summary.

3. How does volume affect production?
Canonical (small system i.e. p-p):
Quantum Numbers conserved exactly.
Computations take into account energy to create companion to ensure conservation of strangeness.
Relative yields given by ratios of phase space volumes
Pn/Pn’ = fn(E)/fn’(E)
Grand Canonical limit (large system i.e. central AA):
Quantum Numbers conserved on average via chemical potential Just account for creation of particle itself.
The rest of the system “picks up the slack”.
When reach grand canonical limit strangeness will
saturate.
Not new idea pointed out by Hagedorn in 1960’s
(and much discussed since)

4. In agreement with T=60 MeV
SIS energies
Pion density
n(p) = exp(-Ep/T)
Strangeness is conserved!
Kaon density – need to balance strangeness
NN N Λ K+
n(K+) ~ exp(-EK+/T)*
(gL V ∫ d3p/(2p)3 exp[-(EΛ-µB)/T]
+ K- term)
KaoS M. Mang et al.
C: N ~ V2 (V 0)
GC: N ~ V (V )
Assume V ~ Npart
Pions/Apart constant
grand-canonical!
Kaons/Apart rising
canonical!
In agreement with T=60 MeV
J. Cleymans, H. Oeschler, K. Redlich, PRC 59 (1999)

5. Predictions at higher energies
Canonical suppression increases with increasing strangeness
Canonical suppression
increases with decreasing energy
σ(Npart) / Npart = ε σ(pp) ε > 1 Enhancement!

6. Top SPS energies NA57, √sNN = 17.3 GeV
We seem to understand what is happening

7. But then at √s= 8.8 GeV
NA57 (D. Elia QM2004)
C to GC predicts a factor larger X- enhancement at √sNN =8.8 GeV than at 17 GeV
Perhaps yields don’t have time to reach limit – hadronic system?

8. But does it over saturate or ONLY just reach saturation?
And then at 200 GeV...
p,K,p
p,K,p,L,X
STAR Preliminary
Au-Au √s=200 GeV
But does it over saturate or ONLY just reach saturation?
L not flat any more!

9. What happens to other particles?
p – Npart scaling
p – slight increase
phase space suppression
of baryons?
K0s – only small phase space
suppression of strange
mesons?
Not flat with centrality
Containss and s quark, so not strange
should show no volume dependence
What about the f?
factor 2 increase relative to p-p

10. Normalized to unity for 0-5% data
Is there a scaling?
The more strangeness you add the less it scales with Npart.
Npart scaling
Normalized to unity for 0-5% data

11. Normalized to unity for 0-5% data
Is there a scaling?
The more strangeness you add the less it scales with Npart.
The larger strangeness content scales better with Nbin.
Still not perfect.
Look at pT dependence.
Nbin scaling
Normalized to unity for 0-5% data

12. Rcp of strange particles
Baryons and mesons are different
Rcp

13. RAA of strange particlesh-
K±, K0s, f and h- all scale similarly
p, L, X show hierarchy.
Phase space suppression in p-p fighting jet suppression in Au-Au.

14. RAA of strange particlesh-
Particles with strange quarks scale differently to non-strange
and as a fn of pT.

15. s quarks have different scaling?
How about scaling according
to quark content?
u, d – scale with Npart
– already observed.
s – scale with Nbin
– appears better for strange
particles.
K0s – 1/2*Npart + 1/2*Nbin
p – Npart
L – 2/3*Npart + 1/3*Nbin
– 1/3*Npart + 2/3*Nbin
f – Nbin
W – Nbin
Pretty good!
Does strangeness “see” a different
correlation volume?
f – Npart

16. Normalized to unity for 0-5% data
How about at SPS?
Again :
The more strangeness the less the particle scales with Npart.
Nbin scaling not correct either.
u,d vs s quark scaling,
not bad except for most peripheral bin - errors large.
Nbin scaling
Npart scaling
Normalized to unity for 0-5% data

17. Summary
Appear to have strangeness saturation at most central top RHIC energies but not before (gs = 1).
Seems that X and W freeze-out differently as a function of centrality.
There is a different scaling for strange vs non-strange particles.
Can see evidence of phase space suppression in RAA.
Do s quarks “see“ a different correlation volume to light quarks?
Our simple thermal pictures are only approximately correct.
The devil is in the details but we have the data to figure it all out.