1. Helen Caines Yale University SQM – L.A.– March 2006 Using strange hadron yields as probes of dense matter. Outline Can we use thermal models to describe the data? Can we describe the multiplicity trends? How do the bulk effects extend into the high p T regime?

2. Helen Caines SQM – L.A. - March 2006 2 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)

3. Helen Caines SQM – L.A. - March 2006 3 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%).

4. Helen Caines SQM – L.A. - March 2006 4 The results RatioSTAR Preliminary          p/p      p                  1.01±0.02 0.96±0.03 0.77±0.04 0.15±0.02 0.082±0.009 0.054±0.006 0.041±0.005 (7.8±1) 10 -3 (6.3±0.8) 10 -3 (9.5±1) 10 -4 1.01±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

5. Helen Caines SQM – L.A. - March 2006 5 “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 -10.3 ± 4.5 MeV T154 ± 4 MeV ss 1.05 ± 7 Au-Au √s NN = 200 GeV STAR Preliminary

6. Helen Caines SQM – L.A. - March 2006 6 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

7. Helen Caines SQM – L.A. - March 2006 7 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

8. Helen Caines SQM – L.A. - March 2006 8 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 K. Redlich Au-Au √s NN = 200 GeV

9. Helen Caines SQM – L.A. - March 2006 9 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

10. Helen Caines SQM – L.A. - March 2006 10 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

11. Helen Caines SQM – L.A. - March 2006 11 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 = 1.1 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

12. Helen Caines SQM – L.A. - March 2006 12 PHOBOS: Phys. Rev. C70, 021902(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 STAR Preliminary Similar enhancement for one s hadrons Au-Au √s NN = 200 GeV

13. Helen Caines SQM – L.A. - March 2006 13 Can we describe √s dependence? N.B.: SPS energy only 17 GeV There’s a correlation between dN ch /d  and N part /2 If know n pp can predict yield at any  N part  small dotted lines are: dN ch /d  n pp (1-x)N part /2 + xN bin n pp = Yield in pp = 2.29 ( 1.27) x = 0.13 PHOBOS: Phys. Rev. C70, 021902(R) (2004)

14. Helen Caines SQM – L.A. - March 2006 14 Strangeness and dN ch /d  SPS and RHIC data follows similar curves as a func. of dN ch /dη at mid-rapidity NA57 dN ch /dη (pBe) =1.64 STAR dN ch /dη (pp) =2.12 Look at yields relative to pp STAR Preliminary Solid – STAR Hollow – NA57 Entropy alone seems to drive much of the soft physics

15. Helen Caines SQM – L.A. - March 2006 15 R AA – Beyond the bulk Effect increases as strange content of baryon increases. Canonical suppression in p+p? R cp  R aa √s NN = 200 GeV STAR Preliminary √s NN = 200 GeV

16. Helen Caines SQM – L.A. - March 2006 16 R AA for central and peripheral data Peripheral and central data both show an enhancement Peripheral data is more enhanced – Cronin effect? Au-Au √s NN = 200 GeV STAR Preliminary Au-Au √s NN = 200 GeV STAR Preliminary

17. Helen Caines SQM – L.A. - March 2006 17 R AA - A mocked up string picture does well Topor Pop et al. hep-ph/0505210 HIJING/BBar + K T ~ 1 GeV Strong Color Field (SCF) qualitatively describes R AA. SCF - long range coherent fields SCF behavior mimicked by doubling the effective string tension SCF only produced in nucleus- nucleus collisions R AA ≠ R CP Are strong color fields the answer?

18. Helen Caines SQM – L.A. - March 2006 18 Nuclear modification factors - R CP √s NN =200 GeV √s NN =62 GeV 0-5% 40-60% 0-5% 40-60% NA57, PLB in print, nucl-ex/0507012 √s NN =17.3 GeV First time differences between  and   B absorption? Recombination or different “Cronin” for  and K at SPS?

19. Helen Caines SQM – L.A. - March 2006 19 STAR Preliminary NA57: G. Bruno, A. Dainese: nucl-ex/0511020 Baryon/meson splitting at SPS and RHIC is the same 62 GeV Au+Au data also follows the same trend Recombination present in all systems? The R cp double ratio What about other centralities?

20. Helen Caines SQM – L.A. - March 2006 20 Conclusions Not all thermal models are the same – even when you try and make them so. The enhancement of strangeness as a function of centrality CAN be described– scales with N part 1/3 NOT N part Non-strange particles are enhanced – NOT predicted by phase space models. Using dN ch /dη better than N part. This is a physical observable unlike N part. The phase space effects of p-p extend into high p T regime. Baryon/meson splitting energy independent.

21. Helen Caines SQM – L.A. - March 2006 21 Multiplicity scaling with log(√s) PHOBOS White Paper: Nucl. Phys. A 757, 28, nucl-ex/0410022 If I can describe dN ch /d  as function of  √s Can we describe other observables in terms of dN ch /dη ? dN ch /dη - strongly correlated to the entropy of the system!

22. Helen Caines SQM – L.A. - March 2006 22 HBT and dN ch /d  HBT radii ~linear as a function N part 1/3 Even better in (dN ch /d  ) 1/3 power 1/3 gives approx. linear scale nucl-ex/0505014 M.Lisa et al. Scaling works across a large energy range