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Strangeness and entropy

Strangeness and entropy. Centrality dependence. Solid – STAR Au-Au √s NN = 200 GeV Hollow - NA57 Pb-Pb √s NN = 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.

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Strangeness and entropy

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  1. Strangeness and entropy

  2. Centrality dependence Solid – STAR Au-Au √sNN = 200 GeV Hollow - NA57 Pb-Pb √sNN = 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 √sNN = 200 GeV K. Redlich

  4. Centrality dependence Correlation volume: V= (ANN)·V0 ANN = Npart/2 V0 = 4/3 p·R03 R0 = 1.1 fm proton radius/ strong interactions STAR Preliminary T = 170 MeV T = 165 MeV Au-Au √sNN = 200 GeV Seems that T=170 MeV fits data best – but shape not correct K. Redlich

  5. Varying T and R Au-Au √sNN = 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 p·R03 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 √sNN = 200 GeV Seems to be a “linear” dependence on collision geometry K. Redlich

  7. More on flavour dependence of E(i) STAR Preliminary PHOBOS: measured E(ch) for 200 and 19.6 GeV Enhancement for all particles? PHOBOS: Phys. Rev. C70, 021902(R) (2004) Au-Au √sNN = 200 GeV Yes – not predicted by model Similar enhancement for one s hadrons

  8. Hagedorn temperature (1965) filled: AA open: elementary [Satz: Nucl.Phys. A715 (2003) 3c • 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 √s ↔ 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 √s • Approximate EOS for that of massless pions. • Assume blackbody • s = S/V related to e s = Fn(√s)

  11. Entropy in Heavy Ion > Entropy in p-p? Nch as measure of entropy J.Klay Thesis 2001 Different EOS? QGP?

  12. Heavy-ion multiplicity scaling with √s There is a scaling over several orders of magnitude of √s i.e. As function of entropy PHOBOS White Paper: Nucl. Phys. A 757, 28

  13. HBT radii <kT>≈ 400 MeV (RHIC)<kT>≈ 390 MeV (SPS) nucl-ex/0505014 Lisa et al. No obvious trends as fn of √s p 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 Entropy determines radii

  14. Eccentricity and low density limit PHENIX preliminary 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

  15. Fluctuations matter PHOBOS QM2005 Important for all Cu-Cu and peripheral Au-Au

  16. Now see scaling Energy range scanned from √s= 4-200 GeV Again dN/dy i.e. entropy important “low density limit” scaling now works

  17. Strangeness vs entropy L W X Solid – STAR Au-Au √sNN = 200 GeV Hollow - NA57 Pb-Pb √sNN = 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

  18. LHC prediction I 6 5 5.5 TeV 1000 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 I’m not in the low density limit any more so v2/e ~ 0.2

  21. LHC prediction IV dNL/dy = dNL/dy ~20-30 dNX/dy = dNX/dy ~4-6 dNW/dy = dNW/dy ~0.5-1 L L W W X X Most central events: dNch/dh ~1200 03

  22. Models readily available to experimentalists

  23. 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%).

  24. The results Au-Au √sNN = 200 GeV after feed-down increase s decrease T 1  error Similar T and s Significantlydifferent errors. Not identical and feed-down really matters

  25. “Best” predictions (with feed-down) 0-5% Au-Au √sNN = 200 GeV STAR Preliminary

  26. Predictions from statistical model Behavior as expected

  27. Comparison between p-p and Au-Au Au-Au √sNN = 200 GeV STAR Preliminary p-p √s = 200 GeV STAR Preliminary Canonical ensemble

  28. Conclusions • dNch/dh is strongly correlated with entropy • dNch/dh scales as log(√s) • 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

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