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Statistical Models and STAR’s Strange Statistical Models and STAR’s Strange DataData
Sevil SalurSevil Salur
Yale University
for the STAR Collaboration
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.
200 GeV Au+Au
ssssss200 GeV Au+Au
udss200 GeV Au+Au
dssss200 GeV Au+Au
200 GeV p+p 200 GeV p+p
The Corrected ParticleSpectra 200 GeV 200 GeV p 200 GeV
(u(us+s+ddss))
((ssss)) *(1520) *(1520) (ud(udss))
**(uu(uuss))
K*200 GeV
* 200 GeV 200 GeV * 200 GeV
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
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.
/ ratios are approximately independent of the system
size at RHIC energies.
Strange ParticleRatios vs System Size
Re-scattering and regeneration is needed ! t > 0, constant for different centralities!Regeneration σ(K*) > σ(*)
Thermal Models Used Models Used 4 parameter Fit SHARE V1.2 THERMUS V2
Authors M. Kaneta et al G. Torrieri, J. Rafelski et. al.
S. Wheaton and J. Cleymans
Language Fortran Fortran C++
Ensemble Grand Canonical Grand Canonical Canonical and Grand Canonical
Parameters T, 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 1 Free Parameter 1
Feed Down possible default 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)
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)
Consistency check of models…
Ratio STAR data
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
all models predict similar T and swith different errors.
They are not identical.
add feed-down increase in s decrease in T
1 error
Thermal Model Predictions without feed-down
T 178 ± 7 MeV
s 0.85 ± 0.05
r 15 ± 10 fm
B (4.3 ± 1.1) X 10-2 MeV
S (1.8 ± 0.8) X 10-2 MeV
Q (-1.9 ± 0.9) X 10-2 MeV
Particle ratios are represented except .
Particle ratios are well described for Tch=177 MeV except the */
Thermal Model Predictions with feed-down
T 168 ± 6 MeV
s 0.92 ± 0.06
r 15 ± 10 fm
B (4.5 ± 1.0) X 10-2 MeV
S (2.2 ± 0.7) X 10-2 MeV
Q (-2.1 ± 0.8) X 10-2 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
Thermal Model Predictions with feed-down
T 171 ± 9 MeV
s 0.53 ± 0.04
r 3.49 ± 0.97 fm
B and Q = 2, S = 0 T 168 ± 6 MeV
s 0.92 ± 0.06
r 15 ± 10 fm
B (4.5 ± 1.0) X 10-2 MeV
S (2.2 ± 0.7) X 10-2 MeV
Q (-2.1 ± 0.8) X 10-2 MeV
Particle ratios are represented except .
Particle ratios are well described except the */T is same for pp and AuAu
J. Cleymans hep-ph 0212335
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%
and yields in AuAurelative 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 √sNN =17.3 GeV collisions.
• Bands from Redlich assuming T=160-175 MeV
System Size Dependence at 200 GeV
Correlation volume not well modelled by Npart
Is the scaling more important than normalization ?
K. Redlich – private communication
Solid – STAROpen – NA57
1
2/31/2
Correlation volume:
V= (ANN)a ·V0
ANN = Npart/2 V0 = 4/3 ·R0
3
R0 = 1.1 fm proton radius/strong interactions
T = 165 MeV a = 1a = 2/3 - area drives yields
a = 1/2 - best fit
s-Quarks Have Different Scaling!
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
– 2/3*Npart + 1/3*Nbin
– 1/3*Npart + 2/3*Nbin
– Nbin
– Nbin
Npart
Does strangeness “see” a significant NBin contribution?
Normalized to central data
is puzzling!
Helen Caines SQM 2004
s-quark
Ordering with strangeness content!
Mesons (h+ + h-, K0s , ) follow
similar trends.
Strange baryons don’t show suppression.
Rcp Raa for strange baryons. Canonical suppression in p+p …?
RAA of Strange Particles
STAR PreliminaryAu+Au
p+p
0-5%
√sNN=200 GeV
Particles with strange quarks scale differently than non-
strange!
Nuclear Modification Factor Rcp
0-5%
40-60%Y-4 K0
s
√sNN=200 GeV
Baryons and mesons are different !
62 GeV Rcp shows less suppression.
√sNN=62 GeV 0-5%
40-60%
Baryon and meson suppression sets in at different pT .
Phys. Rev. Lett. 92 (2004) 052302 Au+Au √sNN=200 GeV
Au+Au √sNN=62 GeV
STAR Preliminary
Nuclear Modification Factor Rcp
Coalescence vs Fragmentation?
0-5%
40-60%
Baryon and meson suppression sets in at
different pT .
Y-4 K0s
√sNN=200 GeV
Baryon and meson suppression sets in at
same quark pT .
0-5%
40-60%
√sNN=200 GeV
Nuclear Modification Factor Rcp
Coalescence vs Fragmentation?
0-5%
40-60%
Baryon and meson suppression sets in at
different pT .
Y-4 K0s
√sNN=200 GeV
0-5%
40-60%
√sNN=200 GeV
For quark pT 0.8-1.2 GeV
pT of the quark 0.8-1.2 GeV baryon pT (2.4-3.6) meson pT (1.6-2.4)
get the yields fit the ratios to thermal models and compare with all.
1 With K/
K/p ratio effect on the fits!
Ratio STAR data
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
Ratio STAR data
p/pp
1.01±0.02
0.96±0.03
0.77±0.04
0.082±0.009
0.054±0.006
0.72±0.024
(7.8±1) 10-3
0.818±0.054
1.01±0.08
K/ reduces the error on s
With K/
Without K/
1 With K/
Quark pT (0.8-1.2) range!
Ratio STAR data
p/p p
1.01±0.02
0.96±0.03
0.77±0.05
0.137±0.013
0.156±0.015
0.72±0.024
(2.9±0.3) 10-2
0.818±0.054
1.01±0.08
K/ reduces the error on s
With K/
Without K/
with feed-down
T and s increases for (0.8-1.2)
1 error
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 pT .
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 pT) 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?
Investigation of strange particle yields and ratios. Comparison of Thermal Models
Thermus, Share and Kaneta et al. The effect of feed-down contributions
RAA comparison with RCP
Investigation of strangeness ordering. Is there a scaling in Au+Au production for the strange
quarks? N Participants vs N Binary ?
Outline
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 pT spectra particle ratios
Statistical models are used to predict the equilibrium properties
Over all range data from my fits!
Ratio STAR data
p/p p
1.01±0.02
0.96±0.03
0.77±0.05
0.102±0.01
0.056±0.006
0.72±0.024
(6.8±0.7) 10-3
0.818±0.054
1.01±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
Fig. 1: QuestionsSolid – 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 Npart calc?