1. Chemical fit at RHIC Masashi Kaneta LBNL
Workshop on Thermalization and Chemical Equilibration in Heavy Ions Collisions at RHIC (July 20-21, 2001 at BNL)
Chemical fit at RHIC
Masashi Kaneta
LBNL
I talk about thermal models at RHIC.
In this talk, I will concentrate chemical freeze-out issues.
Masashi Kaneta, LBNL

2. Many thanks to V.Koch, H.G.Ritter, N.Xu (LBNL), Z.Xu (BNL),
and Organizers
At first, I would like to say many thanks to Nu Xu, Hans Georg Ritter, Volker Koch and Zhangbu Xu for discussions.
And of cause, thank to Organizers invited me to the conference.
Masashi Kaneta, LBNL

3. Outlook Introduction Model Data Freeze-out parameters
Model uncertainties
Summary
Open issues
I will start introduction, model descriptions, RHIC data, chemical freeze-out parameters
Model uncertainties and then summarize this talk.
After that, I address open issues.
Masashi Kaneta, LBNL

4. Introduction Bulk properties of the heavy ion collisions
Statistical approach for particle production
Dynamical information – may be lost?
Chemical freeze-out
occurs at an uniform condition? <E>/<N> ~ 1GeV
SIS (<1GeV), AGS (~5 GeV), SPS (~20 GeV), and RHIC (130 GeV)
The study for RHIC data
P. Braun-Munzinger,D.Magestro, K. Redlich, and J. Stachel, hep-ph/
W. Florkwski, W. Broniowski, and M. Michalec, nucl-th/
F. Becattini, workshop in Trento, June, 2001.
N. Xu and M. Kaneta, nucl-exp/
We want to study bulk properties of the heavy ion collisions to investigate of QGP existence.
What is tool for that?
To understand system in heavy ion collisions,
we have many tools, for example, hydorodynamics, thermo-dynamics and so on.
Here I will address statistical approach for particle production.
Of cause, the dynamical information may be lost.
This approach, so called chemical freeze-out study is established well by many physicists.
One argue is the chemical freeze-out seems to occur an uniform condition at Energy per particle
is about one GeV.
Is it true at RHIC? Let’s look at RHIC data.
And the chemical freeze-out study for RHIC data are done by four collaborations.
One is by the famous peoples, Braun-Munzinger, Redlich and Stachel’s collaboration and
this is reference.
The second one is Polish group.
The next is Becattini who is famous and made progress to apply statistical model to e+e-, ppbar and pp collisions.
The last one. Also famous Nu.Xu and me.
Masashi Kaneta, LBNL

5. Model Hadron resonance ideal gas
Refs. J.Rafelski PLB(1991)333
J.Sollfrank et al. PRC59(1999)1637
Hadron resonance ideal gas
Particle density
of each particle
Qi : 1 for u and d, -1 for u and d
si : 1 for s, -1 for s
gi : spin-isospin freedom
mi : particle mass
Tch : Chemical freeze-out temperature
mq : light-quark chemical potential
ms : strangeness chemical potential
gs : strangeness saturation factor
All resonances and unstable particles are decayed
Let’s me explain the model.
Here we think about hadron resonance ideal gas.
The particle density of each particle species can be described by this formula
and I applied Boltzmann distribution.
This shows particle density as a function of temperature, potentials and strangeness saturation factor, gamma_s.
What is meaning of gamma_s?
If gamma_s is equal to one, the system in fully equilibration of strangeness.
The other variable is particle characteristics, number of quarks, spin-isospin freedom and particle mass.
We assumed resonance gas. However, measured ratios are included decay effect of resonances
and also unstable particle such as strange baryons.
Then, we consider decay effect and obtain particle ratios as a function of Tch, muq, mus, and gamma_s.
I want to mention one thing here.
The fraction of accepted decayed particle is basically unknown factor.
We need an assumption for this fraction and I will discuss this effect later..
Comparable particle ratios to experimental data
Masashi Kaneta, LBNL

6. Model (cont.) Hadron resonance ideal gas
including higher mass resonances(1.7GeV)
For mid-rapidity, no requirement of
Strangeness neutrality
Charge/Isospin conservation
, , , , ’, , f0(980) , a0 (980), h1(1170), b1 (1235), a1 (1260), f2(1270), f1 (1285), (1295),
(1300), a2(1320), f0(1370), (1440), (1420), f1 (1420), (1450), f0 (1500), f1 (1510), f2’(1525),
(1600), 2(1670), (1680), 3(1690), fJ(1710), (1700)
p, n, N(1440), N(1520), N(1535), N(1650), N(1675), N(1680), N(1700)
(1232), (1600), (1620), (1700)
K, K*, K1(1270), K1(1400), K*(1410), K0*(1430), K2*(1430), K*(1680)
, (1450), (1520), (1600), (1670), (1690)
, (1385), (1660), (1670)
, (1530), (1690) 
The model considered resonances upto 1.7GeV of particle mass.
This is list of hadrons and only particle is shown.
So far, some papers required strangeness neutrality and charge, isospin conservation
for SIS to SPS data.
However, The RHIC data currently don’t have whole rapidity distributions of identified particle,
therefore those constrains are not necessary.
Masashi Kaneta, LBNL

7. Ratio data Central Peripheral K+/K- 1.13  0.01  0.06 (STAR)
1.29   (PHENIX)
1.10   (PHOBOS)
1.12   (BRAHMS)
1.11   (STAR)
1.52   (PHENIX)
p/p
0.61   (STAR)
0.61   (PHENIX)
0.60   (PHOBOS)
0.64   (BRAHMS)
0.68   (STAR)
0.63   (PHENIX)
/
0.70  (STAR)
0.88  (STAR)
+/-
0.82  (STAR)
-/+
0.95   (BRAHMS)
1.00   (PHOBOS)
p/-
0.080  (STAR)
0.050  (STAR)
K-/-
0.150  (STAR)
0.101  (STAR)
K*0/h-
0.060   (STAR)
0.058   (STAR)
(K*0+K*0)/2 h-
0.058   (STAR)
I summarized ratios from Quark Matter transparencies, proceedings from BRAHMS, STAR, PHENIX, and PHOBOS.
These are in central collisions and peripheral collisions.
Next I will show you fit results for the ratios.
Red : the values from slide of QM Black : PRL (including submitted)
Blue: the values from figure in proceedings of QM2001
Masashi Kaneta, LBNL

8. Freeze-out parameters
Central
Peripheral
Tch [MeV]
q [MeV]
s [MeV] s
2/dof
186  8
16.7  1.7
1.2  2.4
0.92  0.04
1.9 / 5
147  2
8.8  1.6
-2.9  3.0
0.60  0.02
4.8 / 2
 [MeV/fm3]
 [1/fm3]
P [MeV/fm3]
1160 
0.99 
184 
171 
0.21  0.02
31  3
450
340 21 19
0.32
0.25 69 52
Here we go.
The freeze-out parameters of central and peripheral collisions are listed.
The errors are estimated as chi square minimum plus one.
As I mentioned before, there is assumption about fraction of accepted decayed particle in measurement.
Here, I assumed 50% of decayed particle by week feed-down is contaminated in particle ratios.
We can see the temperature in central collisions is higher than peripheral collisions.
The light-quark chemical potential in both collisions is higher than lower energy.
And muq in central collisions is larger than peripheral reflected baryon density.
The mus is consistent with 0 in both.
This means the chemical freeze-out at RHIC is closer to hadron gas limit, because mus=0 is limit of pure hadron gas.
The most interesting thing is the gamma_s.
It is 0.9 in central and 0.6 in peripheral collisions.
Remember, this values are always less than about 0.7 in AGS, SPS energy and LEP e+e-, SppbarS and Tevatron pp collisions.
Now, we are close to 1 in central collisions.
The bottom three values are energy density, particle density and pressure.
There is the difference between central and peripheral collisions.
However, the energy per particle is 1.16 in central collisions and 0.85 GeV in Peripheral.
Those values are consistent with what we expected from analysis of SIS to SPS energy.
Note: The errors are estimated as 2min+1
The feed-down factor of 0.5 is assumed.
Masashi Kaneta, LBNL

9. Ratios, experiment vs. model
Central
Peripheral
The comparison data and fit results.
If the model describe particle ratios perfectly, the point will stay on this line.
Almost ratios stay of line with in error bar, however K* to h- ratio deviate from line.
Masashi Kaneta, LBNL

10. Strange baryon ratios Central see also J. Zimanyi et al,
hep-ph/
(quark coalescence)
Here I would like to compare anti-baryon to baryon ratio in SPS to RHIC energy.
The circles are data and the star is model predictions.
You can see anti-baryon to baryon ratios are well described by thermal model.
And the Omegabar-Omega ratio is close to one.
It is consistent with STAR data shown in this morning.
Masashi Kaneta, LBNL

11. Systematics Central collisions Temperature increases with beam energy
Lattice QCD
predictions
Central collisions
This analysis
P.Braun-Munzinger et al.
W. Florkowski et al.
Temperature increases
with beam energy
and being close to phase
boundary
Neutron star
Now we can see Systematics of chemical freeze-out.
The chemical freeze-out point is plotted as a function of temperature and baryon chemical potential.
The RHIC points are here, from Braun-Munzinger et al, W.Florkowski et al, and this analysis.
This box is lattice QCD prediction of critical temperature.
And Neutron star stays here, normal nucleon density is black circle.
and the red dash curve is phase boundary and the band shows the uncertainty by model.
The SIS to SPS points stay on this dot line as energy per particle is about one GeV.
Now we can see the RHIC data also stay on this line within error bar.
parton-hadron phase boundary
<E>/<N>~1GeV, J.Cleymans and K.Redlich, PRC60 (1999)
Masashi Kaneta, LBNL

12. } Model uncertainties Mass cut-off Boltzmann vs. Boson/Fermion
weak }
Mass cut-off
Boltzmann vs. Boson/Fermion
Weak decay feed-down
Depend on particle species (i.e. c )
No equal opportunity to decayed particles
deferent pT kick
Depend on detector
Test of the effect in case of
fraction of accepted weak decay (fW) =0, 0.5, 1.0
Now, Let me move on model uncertainties.
There are discrepancy of chemical freeze-out parameter, especially temperature among 4 analysis.
I checked these three items.
One is mass cut-off. I included upto 1.7GeV mass of particles. Even if I used up to 2GeV,
changes is less than a few percent.
I also compare fit results in case of Boltzmann to Boson/Fermion, this effect is less than a few percent.
The last one a fraction of accepted weak decay.
However, this fraction depend on particle species, that is, c tau.
and no equal opportunity to decayed particles because of deferent pT kick.
This must depend on detector acceptance.
To test this effect, I made a map of parameters in case of factor 0, 0.5 and 1.0.
Because I used factor 0 for Nu’s quark matter talk, however, Braun-Munzinger’s paper used 0.5.
Then we need to see dependence of this fraction.
Masashi Kaneta, LBNL

13. Feed-down effects B [MeV] Tch [MeV] s s [MeV]
Central collisions, top15%
Peripheral collisions, >50%
s [MeV] s
Here, The chemical freeze-out parameters are shown as a function of fraction of accepted weak decay.
The solid and open circle correspond to central and peripheral collisions, respectively.
So you can see there is strong dependence in temperature and much less dependence for potentials and gamma_s.
Now we eventually reach to origin of deference among 4 analysis.
fraction of accepted weak decay
Masashi Kaneta, LBNL

14. Summary Only mid-rapidity ratios used;
With selected fW the Tch and  are consistent with what expected;
Centrality dependence;
Systematic uncertainty needed to be evaluated;
Let me summarize.
The ratio around mid-rapidity used for statistical approach.
The results show stay on what we expected as energy per particle is about one GeV.
The fits to central and peripheral collisions data are shown.
In central collisions, the temperature shows higher than in peripheral.
and small muq and almost zero mus.
The one of the most interesting thing is strange saturation factor is 0.9 in central collisions.
This means the system is close to fully strangeness equilibration in central collisions at RHIC.
Finally, the fraction of accepted week-decay has strong dependence. the effect of feed-down
should be evaluated by experiment to fix the temperature parameter.
And now, I would like to address open issues.
Masashi Kaneta, LBNL

15. Open issues Particle ratios are described by statistical model well
Dynamical information?
Global vs. local equilibration
Connection between Tch and Lattice QCD Tc?
The statistical model describe particle ratios.
But where is dynamical information? for example expansion.
The analysis can be done only round mid-rapidity up-to-now.
On the other hand, almost analyses at SIS to SPS energy are for full yield.
Now, I argue the system is in global equilibration or local.
The tch is similar to critical temperature from Lattice QCD calculation.
Can we direct compare both values?
Masashi Kaneta, LBNL

16. Test: rapidity dependence
Au + Au at 200 GeV (b3 fm)
(a) Temperature: Increasing as the
rapidity width y open up;
(b) Baryon chemical potential:
increase with y;
(c) Strange chemical potential:
decrease with y;
(d) Strange saturation factor:
Thermal parameters depend
on the kinetic cuts!
RQMD(v2.4)
NEXUS(V1.1)
Here is test of rapidity cut dependence of chemical freeze-out parameter for yield to event generators.
You can see there are strong dependences for the parameters.
And the temperature at mid-rapidity is smaller than fit from 4pi yield.
muq is increasing with wider cut. and mus shows opposite tendency between two model.
and gammas is decreasing with cut.
Thermal parameters depend on the kinetic cuts and it mean no global equilibration.
J. Phys. G: Nucl. Part. Phys. 27 (2001) 589, M. Kaneta and N. Xu
Masashi Kaneta, LBNL

17. Open issues Not fully ideal system at 4TC Collective effects ? ???
F. Karsch, hep-lat/
Not fully ideal system at 4TC
Collective effects ?
???
This is recent Lattice QCD calculation.
Even if 4 times of critical temperature, QGP is not ideal gas.
However, hadron gas model is assumed ideal gas.
Can we compare both results?
The both lattice calculation and statistical approach to hadron ratios
do not included collective effects. What is the effect?
Maybe, there are more unknown issues.
With those open issues, I end this talk.
Masashi Kaneta, LBNL