Helen Caines Yale University Strasbourg - May 2006 Strangeness and entropy

Helen Caines Strasbourg – May Centrality dependence We can describe p-p and central Au-Au average ratios. Can we detail the centrality evolution? Look at the particle enhancements. E(i) = Yield AA /Npart Yield pp /2 STAR Preliminary Solid – STAR Au-Au √s NN = 200 GeV Hollow - NA57 Pb-Pb √s NN = 17.3 GeV

Helen Caines Strasbourg – May 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 = MeV assume same T for p-p and Au-Au K. Redlich Au-Au √s NN = 200 GeV

Helen Caines Strasbourg – May Centrality dependence STAR Preliminary K. Redlich Correlation volume: V= (A NN ) ·V 0 A NN = N part /2 V 0 = 4/3  ·R 0 3 R 0 = 1.1 fm proton radius/ strong interactions T = 170 MeVT = 165 MeV Seems that T=170 MeV fits data best – but shape not correct Au-Au √s NN = 200 GeV

Helen Caines Strasbourg – May Varying T and R Calculation for most central Au-Au data Correlation volume: V 0  R 0 3 R 0 ~ proton radius strong interactions Rapid increase in E(i) as T decreases SPS data indicated R = 1.1 fm K. Redlich Au-Au √s NN = 200 GeV

Helen Caines Strasbourg – May N part dependence STAR Preliminary K. Redlich Correlation volume: V= (A NN )  ·V 0 A NN = N part /2 V 0 = 4/3  ·R 0 3 R 0 = 1.2 fm proton radius/ strong interactions T = 165 MeV  = 1 T = 165 MeV  = 2/3 T = 165 MeV  = 1/3 Seems to be a “linear” dependence on collision geometry Au-Au √s NN = 200 GeV

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

Helen Caines Strasbourg – May 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 T c = 158 MeV r(m) (GeV -1 ) Green states of 1967 Red – 4627 states of 1996 m (GeV) filled: AA open: elementary [Satz: Nucl.Phys. A715 (2003) 3c T H ~ 160 MeV T  S =  E increase √s ↔ increase S

Helen Caines Strasbourg – May 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 dN ch /d  is correlated to S

Helen Caines Strasbourg – May Entropy and √s Approximate EOS for that of massless pions. Assume blackbody s = S/V related to  s = Fn(√s)

Helen Caines Strasbourg – May N ch as measure of entropy Entropy in Heavy Ion > Entropy in p-p? J.Klay Thesis 2001 Different EOS? QGP?

Helen Caines Strasbourg – May 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

Helen Caines Strasbourg – May HBT radii Entropy determines radii No obvious trends as f n of √s  HBT radii from different systems and at different energies scale with (dN ch /dη) 1/3 power 1/3 gives approx. linear scale nucl-ex/ Lisa et al. ≈ 400 MeV (RHIC) ≈ 390 MeV (SPS) Works for different m T ranges

Helen Caines Strasbourg – May Eccentricity and low density limit At hydro. limit v 2 saturates At low density limit Apparent complete failure. Especially at low density! Voloshin, Poskanzer PLB 474 (2000) 27 v 2 different as f n N part and energy PHENIX preliminary

Helen Caines Strasbourg – May Fluctuations matter Important for all Cu-Cu and peripheral Au-Au PHOBOS QM2005

Helen Caines Strasbourg – May “low density limit” scaling now works Now see scaling Again dN/dy i.e. entropy important Energy range scanned from √s= GeV

Helen Caines Strasbourg – May Strangeness vs entropy Solid – STAR Au-Au √s NN = 200 GeV Hollow - NA57 Pb-Pb √s NN = 17.3 GeV No scaling between energies But does become ~linear at higher dN ch /d  dN ch /d  n pp ((1-x)N part /2 + xN bin ) n pp = Yield in pp = 2.29 ( 1.27) x = 0.13   

Helen Caines Strasbourg – May PHOBOS White Paper: Nucl. Phys. A 757, TeV = RHICx1.6 Most central events: dN ch /d  ~1200 LHC prediction I

Helen Caines Strasbourg – May LHC prediction II R o = R s = R l = 6 fm Most central events: dN ch /d  ~1200 dN ch /d   ~10.5

Helen Caines Strasbourg – May LHC prediction III Most central events: dN ch /d  ~1200 S ~ 20 But I suspect I’m not in the low density limit any more so v 2 /  ~ 0.2

Helen Caines Strasbourg – May LHC prediction IV dN  /dy = dN  /dy ~20-30 dN  /dy = dN  /dy ~4-6 dN  /dy = dN  /dy ~0.5-1 Most central events: dN ch /d  ~1200      0303

Helen Caines Strasbourg – May Models readily available to experimentalists Models4 parameter Fit SHARE V1.2THERMUS V2 AuthorsM. Kaneta et al. G. Torrieri, J. Rafelski et al. S. Wheaton and J. Cleymans EnsembleGrand Canonical Canonical and Grand Canonical Parameters T,  q,  s,  s T, q, s,  s,  q,  I3, N, C,  C T, B, S, Q,  s, R T,  B,  S,  q,  C,  s,  C, R Feed Downpossibledefault is with % feed-down default is no feed- down (harder to manipulate)

Helen Caines Strasbourg – May First make a consistency check Require the models to, in principle, be the same. 1.Only allow the least common multiple of parameters: T,  q,  s,  s 2.Use Grand Canonical Ensemble. 3.Fix weak feed-down estimates to be the same (i.e. at 100% or 0%).

Helen Caines Strasbourg – May The results RatioSTAR Preliminary          p/p      p                  1.01± ± ± ± ± ± ±0.005 (7.8±1) (6.3±0.8) (9.5±1) ±0.08 after feed-down increase  s decrease T 1  error Not identical and feed-down really matters Similar T and  s Significantly different errors. Au-Au √s NN = 200 GeV

Helen Caines Strasbourg – May “Best” predictions (with feed-down) 0-5% THERMUS  B 45 ± 10 MeV  S 22 ± 7 MeV  Q -21 ± 8 MeV T168 ± 6 MeV ss 0.92 ± 0.06 SHARE  q 1.05 ± 0.05 (23 MeV) ss 1.02 ± 0.08 (5 MeV) T133 ± 10 MeV ss 2.03 ± 0.6 qq 1.65 ± 0.5 ss 1.07 ± 0.2 Kaneta  B 8.0 ± 2.2 MeV  S ± 4.5 MeV T154 ± 4 MeV ss 1.05 ± 7 Au-Au √s NN = 200 GeV STAR Preliminary

Helen Caines Strasbourg – May Predictions from statistical model Behavior as expected

Helen Caines Strasbourg – May Comparison between p-p and Au-Au T171 ± 9 MeV ss 0.53 ± 0.04 r3.49 ± 0.97 fm Canonical ensemble T168 ± 6 MeV ss 0.92 ± 0.06 r15 ± 10 fm Au-Au √s NN = 200 GeV STAR Preliminary p-p √s = 200 GeV STAR Preliminary

Helen Caines Strasbourg – May Conclusions dN ch /d  is strongly correlated with entropy dN ch /d  scales as log(√s) Several variables from the soft sector scale with dN ch /d  HBT v 2 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 N part