1 Statistical Models and STAR’s Strange Data Sevil Salur Yale University for the STAR Collaboration

2 Particle Production and Volume Pointed out by Fermi, Hagedorn in 1960’s (and discussed much more since) Particle production can be described by the phase space! Statistical models are used to estimate the equilibrium properties Trends of particle yields and ratios How good are the thermal model fits? What are T,  s  B parameters? Can the phase space arguments describe the strangeness centrality dependence? Is there a difference in the production of the bulk matter and the non-bulk matter? Canonical (small system i.e. pp): Quantum Numbers conserved exactly. Grand Canonical limit (large system i.e. central AA): Quantum Numbers conserved on average via chemical potential.

GeV Au+Au sss  sss  200 GeV Au+Au s  uds  200 GeV Au+Au ss  dss  200 GeV Au+Au  200 GeV p+p  200 GeV p+p The Corrected Particle  Spectra  200 GeV  200 GeV p 200 GeV  (us+ds)  (ss)  *(1520) (uds)  *  (uus) K*200 GeV  * 200 GeV  200 GeV  * 200 GeV

4 STAR Preliminary s-Baryon production is ~constant at mid-rapidity. STAR Preliminary Strange Baryon Production and Collision Energy…  s-Baryon production equals s-Baryon at RHIC Energies!  s-Baryon rises smoothly at mid-rapidity. s-Baryon Resonance follow the same trend. Au+Au Pb+Pb STAR Preliminary

5 An enhancement in the K/  ratios ~ 50% Strangeness Production and Collision Energy…    independent of system size at 200 GeV and equal to p+p values at lower energies.

6  /  ratios are approximately independent of the system size at RHIC energies. Strange Particle  Ratios vs System Size Re-scattering and regeneration is needed !  t > 0, constant for different centralities! Regeneration σ(K*) > σ(  *)

7 Thermal Models Used Models Used4 parameter FitSHARE V1.2THERMUS V2 AuthorsM. Kaneta et alG. Torrieri, J. Rafelski et. al. S. Wheaton and J. Cleymans LanguageFortran C++ EnsembleGrand Canonical Canonical and Grand Canonical ParametersT,  q,  s,  s T, q, s,  q,  s,  I3, N, C,  C T,  B,  S,  q,  C,  s,  C, R (T B S Q  s R) qq 1Free Parameter1 Feed Downpossibledefault is with % feed-downs default is not with feed-downs (harder to manipulate) Chemical Potential  I paticle anti-particle difference, Phase Space Occupancy  I regulates the sum of particle-anti particle pairs GRAND Canonical: (Large) on average conservation Canonical: (Small) event-by-event conservation =exp(  /T)

8 To make any kind of consistency checks … FIRST: Requirements of the models should be same. Fix parameters … E.g. Set  q to 1 in SHARE, Allow only Grand Canonical Ensemble in THERMUS Either remove all the feed-downs or include to all models with the same amounts. (Tricky One)

9 Consistency check of models… RatioSTAR data          p/p      p                  1.01± ± ± ± ± ± ±0.005 (7.8±1) (6.3±0.8) (9.5±1) ±0.08 all models predict similar T and  s with different errors. They are not identical. add feed-down increase in  s decrease in T 1  error

10 Thermal Model Predictions without feed-down T178 ± 7 MeV ss 0.85 ± 0.05 r15 ± 10 fm  B (4.3 ± 1.1) X MeV  S (1.8 ± 0.8) X MeV  Q (-1.9 ± 0.9) X MeV Particle ratios are represented except . Particle ratios are well described for T ch =177 MeV except the  */ 

11 Thermal Model Predictions with feed-down T168 ± 6 MeV ss 0.92 ± 0.06 r15 ± 10 fm  B (4.5 ± 1.0) X MeV  S (2.2 ± 0.7) X MeV  Q (-2.1 ± 0.8) X MeV Particle ratios are represented except . Particle ratios are well described except the  */  Small  B  No incoming baryon number T is same for pp and AuAu

12 Thermal Model Predictions with feed-down T171 ± 9 MeV ss 0.53 ± 0.04 r3.49 ± 0.97 fm B and Q = 2, S = 0 T168 ± 6 MeV ss 0.92 ± 0.06 r15 ± 10 fm  B (4.5 ± 1.0) X MeV  S (2.2 ± 0.7) X MeV  Q (-2.1 ± 0.8) X MeV Particle ratios are represented except . Particle ratios are well described except the  */  T is same for pp and AuAu J. Cleymans hep-ph The relative strangeness production for Pb+Pb at SPS similar to p+p at RHIC.  s is higher in AuAu An enhancement in the K/  ratios ~ 50%

13  and  yields in AuAu  relative to pp rises. System Size Dependence at 200 GeV Solid – STAR Open – NA57 The enhancements grow with the strangeness of the baryon and centrality. The enhancements are similar to those measured in √s NN =17.3 GeV collisions. Bands from Redlich assuming T= MeV

14 System Size Dependence at 200 GeV Correlation volume not well modelled by N part Is the scaling more important than normalization ? K. Redlich – private communication Solid – STAR Open – NA57  1 2/3 1/2 Correlation volume: V= (A NN ) a ·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 a = 1 a = 2/3 - area drives yields a = 1/2 - best fit

15 s-Quarks Have Different Scaling! Scaling according to quark content? u, d – scale with N part – already observed. s – scale with N bin – appears better for strange particles. K 0 s – 1/2*N part + 1/2*N bin p – N part  – 2/3*N part + 1/3*N bin  – 1/3*N part + 2/3*N bin  – N bin  – N bin N part Does strangeness “see” a significant N Bin contribution? Normalized to central data  is puzzling! Helen Caines SQM 2004

16 s-quark Ordering with strangeness content! Mesons (h + + h -, K 0 s,  ) follow similar trends. Strange baryons don’t show suppression. Rcp  Raa for strange baryons. Canonical suppression in p+p …? R AA of Strange Particles STAR Preliminary Au+Au p+p 0-5% √s NN =200 GeV Particles with strange quarks scale differently than non-strange!

17 Nuclear Modification Factor R cp 0-5% 40-60% Y-4  K 0 s √s NN =200 GeV Baryons and mesons are different ! 62 GeV R cp shows less suppression. √s NN =62 GeV 0-5% 40-60% Baryon and meson suppression sets in at different p T.

18 Phys. Rev. Lett. 92 (2004) Au+Au √s NN =200 GeV Au+Au √s NN =62 GeV STAR Preliminary Nuclear Modification Factor R cp Coalescence vs Fragmentation? 0-5% 40-60% Baryon and meson suppression sets in at different p T. Y-4  K 0 s √s NN =200 GeV

19 Baryon and meson suppression sets in at same quark p T. 0-5% 40-60% √s NN =200 GeV Nuclear Modification Factor R cp Coalescence vs Fragmentation? 0-5% 40-60% Baryon and meson suppression sets in at different p T. Y-4  K 0 s √s NN =200 GeV

% 40-60% √s NN =200 GeV For quark p T GeV p T of the quark GeV baryon p T ( ) meson p T ( ) get the yields fit the ratios to thermal models and compare with all.

 With K/  K/p ratio effect on the fits! RatioSTAR data          p/p      p                  1.01± ± ± ± ± ± ±0.005 (7.8±1) (6.3±0.8) (9.5±1) ±0.08 RatioSTAR data          p/p   p               1.01± ± ± ± ± ±0.024 (7.8±1) ± ±0.08 K/  reduces the error on  s With K/  Without K/ 

 With K/  Quark p T ( ) range! RatioSTAR data          p/p p               1.01± ± ± ± ± ±0.024 (2.9±0.3) ± ±0.08 K/  reduces the error on  s With K/  Without K/  with feed-down T and  s increases for ( ) 1  error

23 Conclusions  Baryon transport is ~ independent of system size at RHIC energies.  Coalescence can explain the meson baryon difference at 62 GeV collisions too. Baryon and meson suppression sets in at same quark p T.  Feed down corrections from weak decays are important.  T is similar for pp and AuAu collisions. While  s of pp collisions at RHIC is smaller than AuAu at RHIC, it is similar to that of PbPb at SPS.  Where quark coalescence seems to dominate (intermediate p T ) T and  s show an increase. It looks like these particles come from a hotter source.  Particles with s-quarks appear to scale differently than non-s quarks. Maybe s-quarks “see“ a different correlation volume than light quarks?

24 EXTRAS…

25 Investigation of strange particle yields and ratios. Comparison of Thermal Models Thermus, Share and Kaneta et al. The effect of feed-down contributions R AA comparison with R CP Investigation of strangeness ordering. Is there a scaling in Au+Au production for the strange quarks? N Participants vs N Binary ? Outline

26 Particle Production and Volume Canonical (small system i.e. pp): Quantum Numbers conserved exactly. Computations take into account energy to create companion to ensure conservation of strangeness. Grand Canonical limit (large system i.e. central AA): Quantum Numbers conserved on average via chemical potential. Account only creation of particle itself. The rest of the system “picks up the slack”. When reach grand canonical limit strangeness saturate Pointed out by Fermi, Hagedorn in 1960’s (and much more discussed since) Particle production can be described by the phase space! Need to measure p T spectra  particle ratios Statistical models are used to predict the equilibrium properties

27 Spectra with exponential fits √s NN =200 GeV AuAu Collisions

28

29 Over all range data from my fits! RatioSTAR data          p/p p               1.01± ± ± ± ± ±0.024 (6.8±0.7) ± ±0.08 T and  s parameters are predicted to be the same in both sets of ratios! with feed-down little effect on T and  s

30 Fig. 1: Questions Solid – STAR Open – NA57 Is reason that protons don’t sit at unity due to lack of feed-down correction from Lambda? Is this a problem when taking ratios? Different feed- down for p-p than Au-Au? Also questions about the highest two centrality bins as them see high for all our data. Is there a problem with our N part calc?