Progress of Theoretical Physics Supplement No. 129, 1997
167
Chemical Property in Heavy Ion Collisions
Masashi
KANETA
for NA44 Collaboration*)
Department of Physics, Hiroshima University, Higashi-Hiroshima 139, Japan
(Received August 31, 1997)
K-1 K+ and PIP ratios measured in 158 A-GeV Pb + Pb collisions are shown as a
function of centrality and transverse momentum ( Pt). Little significant centrality dependence
in neither K-1 K+ nor PIP ratios are observed and they are almost constant as a function
of Pt. The chemical freeze-out temperature Tch and the chemical potentials for both light
and strange quarks (J-tq, J-ts) are extracted by comparing the present data with simple model
predictions. The J-tq, I-ts and Tch from the NA44 are compared with those obtained from
similar analysis of SPS S + A and AGS Si + A data. The chemical freeze-out temperature
Tch in CERN energy is higher than thermal freeze-out temperature Tro which is extracted
from transverse momentum distribution of charged hadrons. In AGS energy Tch is close to
Tro§1.
Introduction
A study of particle ratios will address the physics of particle production mechanism in high energy heavy ion collisions. In the collisions, the energy of beam makes
the nucleus violent collisions. The state is in high temperature and/or high pressure.
Hadronization occurs and hadrons collide with each other. Thus, there are particle
creation and absorption. The process of particle production is in a complex system
and had better to be discussed with time evolution and space expansion. However,
it seems to be not bad idea to check chemical equilibrium assumption as a first step.
Assuming particle ratios measured is conserved after the end of chemical equilibrium state (chemical freeze-out), we can check the chemical equilibrium assumption
by comparing particle ratios with model predictions.
Later, particle creation and absorption stop and the system changes to random
motion. When the system becomes so big that the hadrons are free particle, they
go out (thermal freeze-out). In SPS and AGS experiments, the transverse mass
distributions of hadrons suggest that there is local thermal equilibrium state and
some indications of the transverse flow.
§2.
NA44 experiment
The NA44 focusing spectrometer is designed to measure particle momentum
distribution of charged hadrons around mid rapidity. A Cherenkov beam counter
(CX) provides the time of flight (TOF) start time with a resolution of about 30 ps l)
and the total TOF resolution is less than 100 ps. Particle identification is done
by TOF and two different threshold Cherenkov counter; momentum resolution 8pjp
•) NBI, LANL, Columbia, Nantes, Hiroshima, CERN, Rusjer Boskovic, Ohio, Vienna Technica, Lund,
Texas A&M, BNL.
168
M. Kaneta for NA
44
Collaboration
is about 0.5 % and the centrality is measured by multiplicity counters behind the
target. Details about the spectrometer may be shown in Refs. 2)rv4).
§3.
Particle ratios and discussion
3.1. K- I K+ and pjp ratios as a function of Pr and centrality
The NA44 experiment measures charged kaons and protons around mid-rapidity
(Ytab ;::: 3). There is no difference of acceptance between same mass particles, then
we need no acceptance correction for
0 ... =6-8.5%
" ... =3.5%
K- I K+ and f51P ratios. The event cen0.9
trality r7triglageom is determined by a
..
0.7
j
multiplicity counter behind the target.
1
~ 0.8
+ t ~ 1ij ~ ~
1
+/,+,tt4~
ii,~
#1
t+
t++
tl,t
•
It##
++++++J.J~~~~~i
':.:: o.
We select three regions; the most central
I
j
0.•
3.5 %, further 3.5-6.0 % and 6.0-8.5 %.
0.
'
N,44.f. Preliminarv
Figure 1 shows K- IK+ and PIP ra0.14
0.1 2
tios as a function of centrality and Pr.
0.
The
general trend of the ratios is almost
1
:-e. 0.08
tt+tdt ttl~,~~1 ~,,!l
++\~~~.~~), t+tHt tf~~~~"~~
•o.. o.oe
+ I
constant
for Pr. We observed little cen0.04
0.0 2
trality dependence in both K- I K+ and
PIP ratios in the top 8.5 % central rePT[GeV]
gion.
Fig. 1. K- / K+ and pjp ratios as a function
We identified the charged hadrons
of centrality and Pr. Horizontal lines show
and their momentum measured ;::: 20 m
the mean ratio.
downstream from target. Thus, we have
to estimate feed-down from resonance
decay on the particle ratios, especially for the f51P ratio.
1
) ••
3.2. Lambda decay effect to proton ratios
We cannot ignore an effect of resonance decay; for example, RQMD (Vl.08)
shows Alp;::: 0.4 and Alp;::: 0.6 around mid-rapidity in central Pb + Pb collisions.
We estimate the A and A feed-down effect to f51P by a Monte Carlo simulation.
The inputs of simulation are parameterized dNI dy distributions referred
from RQMD (V1.08) and mr slopes
from experimental result. 4 ), 5 ) Figure 2
0.6
shows correction factor of feed-down ef0.4
fect for j5 / p ratio as a function of Pr.
0.2
We can get 'pure f51P ratio' by multiplying
that factor to the measured f51P
0.6
0.8
1
0.2
1.2
0.4
1.4
1.8
PT [GeV]
ratio. To estimate the systematic error, we changed the values of dNidy
Fig. 2. Correction factor of feed-down effect
(±30 %) and mr slope (±10 %) for infor pjp ratio as a function of Pr.
put of simulation, respectively. The error is dominated by changing of dNI dy and not by mr slope. The correction factor
~__J_~--'-"----"-_.___1___-"
• l
·~-"----"-
169
Chemical Property in Heavy Ion Collisions
found to be about 0.9 ± 0.1 and independent of PT.
3.3. Strangeness neutral hadron gas model
Thermodynamics provides us chemical potential and temperature as physical
variable to describe a system in chemical equilibrium. Chemical equilibrium state
in heavy ion collisions have been discussed by almost same idea in many papers, for
example Refs. 6)"'17). We introduce a model in this subsection, taken from Ref.
15). It considered only strangeness neutral hadron gas in equilibrium state with no
space expansion.
If one assumes chemical equilibrium state, the strangeness partition function of
hadron gas is given as a function of light quark, strange quark chemical potential
(J.Lq, ft 8 ), chemical equilibrium temperature Tch, and mass of strangeness. In this
model, we assumed hadron gas including well-known higher mass resonance up
to 1.6 Ge V. The total strangeness should be zero in the hadron gas because of
strangeness conservation in the collisions. That condition gives us J.Ls as a function
of J.Lq for different Tch· The PIP and K- I K+ ratios are re-described by J.Lq, J.Ls and
T; PIP= exp( -6J.LqiT), K- I K+ = exp(-2(J.Lq- J.Ls)IT).
3.4. Comparison with model predictions
Figure 3 shows K- I K+ vs pjp. The lines are model predictions of ratios for
different temperature (150 to 200 MeV with 10 MeV step). The solid circle is from
central Pb + Pb collisions from NA44. The open circle is NA52 minimum bias data
around mid rapidity from Ref. 18). The correction for Lambda decays for proton
ratio is done for only NA44 data. The NA52 point may shift to smaller values, if a
Lambda decay correction is considered.
If a feed-down effect for NA52 minimum bias data is same order with NA44
central data, the PIP ratio changes to about 0.1. In that case, the ratio is decreas-
Pb+Pb
0.8
~~
o.rs
} Strangeness Neutral HG
I
0.7
0
~
0.85
~
0.6
Q
~
f-0
~.
"'"
o:l·
""'
0.04
-t~-
100
NA44 Preliminary (central: top 8.5%)
0.08
0.06
p/p ratio
Fig. 3.
0.1
0.12
'-" S+S
•
Si+Au(Pb),
Phys. Lett. 8344 t 1995143
.& Si+Au,
50
from QM'96
•
0 S+Pb
6 S+W ) Phy~. Rev.
? S+Ag ('5]\\9961 135l
Pbys. Rev C5] C 1996) I 353
't' Si+Au.
Phys Lett 8328(19941499
• > NA52 Preliminary (M.B.)
1
,~~ 1 • ~~~~'~-'-~~
0.02
200
150
¥
0.4
0.35
Pb+Pb. NA44 preliminar~
0 S+Au(W.Pb).
Phys. Leu. B365 (I 99tH I
•
CERN SPS
BNLAGS
•
0.55
250-
0.14
0
.L--~~100 ~. -~00
(l [MeV]
0
Fig. 4. Tch vs Jl-q for S + A, Pb
and Si + A at AGS.
+ Pb at
SPS
170
M. Kaneta for NA
44 Collaboration
ing with increasing centrality, it is compatible with model predictions if chemical
temperatur e is independen t of the centrality. The Tch for NA44 data is found to be
between 170 MeV and 180 MeV. We calculate the chemical potentials for NA44 data
in case of Tch = 175 MeV. /-lq = 81 ± 3 MeV, 1-ls = 30 ± 4 MeV in Pb + Pb central
collisions.
To compare Pb + Pb data with other system and model, we summarized some
data. Figure 4 shows /-lq and Tch for S + A and Pb + Pb at the CERN SPS and
Si +A at the BNL AGS. The point from Ref. 16) is the same model with we used.
The point from Refs. 8), 12) and 17) is not set total strangeness quantum number
equal to zero to extract /-lq and Tch. We can see there is model dependence of the
values for same measured ratio, however there is difference between SPS and AGS
energy. The Tch (/-lq) in SPS energy is higher (lower) than in AGS energy. Roughly
speaking, it shows higher baryon density in AGS energy than SPS energy.
3.5.
Thermal freeze-out temperature
It is well known that the mr distribution of hadron in nuclear collisions shows 1I mr dNI dmr
A
x exp( -mriT), where A is an arbitrary
constant and Tis slope parameter. The
trend of T in heavy ion collisions is discussed in Ref. 19). The slope parameter
T and particle mass m may be described
by the relationship : T = Tro + m(vr?,
where Trois thermal freeze-out temperature and (vr) is averaged transverse flow
velocity. (See Fig. 5.)
The freeze-out temperatur e is independent of the collision system in the
CERN energy region and seems to saturate at Tro = 140 ± 10 MeV. 19 ) The Tro
is lower than Tch. On the other hand,
Tro = 145 ± 15 MeV at AGS and Tch is
close to with Tro.
§4.
>
0.4
BNLAGS
Q)
Q.
Ebeam = 14.6 A GeV/c
Ylab = 1.3
I- 0.3
.....
-
f
Si+Au
Q)
•
Q)
E
~
0.2
CG
a.
Q)
a.
0
I
~ •
+p+Be
0.1
Solid: Positive
(/)
Open: Negative
0
0
2
mass [GeV]
• ; T. Abbott eta!, Phys. Rev. C50 (1994) 1024
•u T. Abbott eta!, Phys. Rev. D50 (1992) 3906
Fig. 5. Slope parameter vs mass at AGS. The
values of slope parameter are referred from
the paper.
Summary
We report K- IK+ and 'PIP ratios as a function of Pr and centrality from Pb +
Pb central collisions. Kaon and proton ratios are almost constant as a function of Pr.
We observe little centrality dependence in either kaon and proton ratios. Assuming
the system is in chemical equilibrium , the chemical equilibrium temperatur e is found
to be Tch ~ 175 MeV for Pb + Pb. From K- I K+ and 'PIP ratios, the chemical
potential of light and strange quark was calculated to be: /-lq ~ 80 MeV and 1-ls ~ 30
MeV, respectively. The chemical equilibrium temperatur e is greater than the freezeout temperatur e. It is not inconsisten t with the point of view from thermodyna mics.
Chemical Property in Heavy Ion Collisions
171
We summarized the value of /-lq and Tch in heavy ion collisions at SPS and AGS.
There is model dependence of P,q and Tch for same collisions system. However, the
general trend is that P,q (Tch) at SPS is lower (higher) than at AGS. The Tch is grater
than Tro in S + A and Pb + Pb collisions at SPS. In AGS, both temperatures are
close to each other.
Acknowledgeme nts
NA44 collaboration thanks the staff of the CERN PS-SPS accelerator complex for their excellent work. We are grateful to the technical staff at CERN and
the collaborating institutes for their valuable contribution. We also wish to thank
for the support given by the Austrian Fonds zur Forderung der Wissenschaftlichen
Forschung; the Science Research Council of Denmark; the Japanese Society for the
Promotion of Science; the Ministry of Education, Science and Culture, Japan; the
Science Research Council of Sweden; the National Science Foundation, the US Department of Energy and theW. B. Keck Foundation.
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