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

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.

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)

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)

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!

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

But then at √s= 8.8 GeV NA57 (D. Elia QM2004) C to GC predicts a factor 4 - 5 larger X- enhancement at √sNN =8.8 GeV than at 17 GeV Perhaps yields don’t have time to reach limit – hadronic system?

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!

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

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

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

Rcp of strange particles Baryons and mesons are different Rcp

RAA of strange particles h- 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.

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

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

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

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.