Hyperon production in Ar+KCl collisions at 1.76A GeV

Abstract

We present transverse momentum spectra, rapidity distribution and
multiplicity of Lambda-hyperons measured with the HADES spectrometer in the
reaction Ar(1.76A GeV)+KCl. The yield of Xi- is calculated from our previously
reported Xi-/(Lambda+Sigma0) ratio and compared to other strange particle
multiplicities. Employing a strangeness balance equation the multiplicities of
the yet unmeasured charged Sigma hyperons can be estimated. Finally a
statistical hadronization model is used to fit the yields of pi-, K+, K0s, K-,
phi, Lambda and Xi-. The resulting chemical freeze-out temperature of T=(76+-2)
MeV is compared to the measured slope parameters obtained from fits to the
transverse mass distributions of the particles.

Full text

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arXiv:1010.1675v2 [nucl-ex] 18 Oct 2010
EPJ manuscript No.
(will be inserted by the editor)
Hyperon production in Ar+KCl collisions at 1.76A GeV
G. Agakishiev6, A. Balanda3,†, B. Bannier5, R. Bassini9, D. Belver16, A. Belyaev6, A. Blanco2, M. B¨ ohmer12,
J. L. Boyard14, P. Cabanelas16, E. Castro16, S. Chernenko6, T. Christ12, M. Destefanis8, J. D´ ıaz17, F. Dohrmann5,
A. Dybczak3, T. Eberl12, E. Epple11, L. Fabbietti11, O. Fateev6, P. Finocchiaro1, P. Fonte2,A, J. Friese12, I. Fr¨ ohlich7,
T. Galatyuk7, J. A. Garz´ on16, R. Gernh¨ auser12, A. Gil17, C. Gilardi8, M. Golubeva10, D. Gonz´ alez-D´ ıaz4, F. Guber10,
M. Gumberidze14, M. Heilmann7, T. Heinz4, T. Hennino14, R. Holzmann4, P. Huck12, I. Iori9,C,†, A. Ivashkin10,
M. Jurkovic12, B. K¨ ampfer5,B, K. Kanaki5, T. Karavicheva10, D. Kirschner8, I. Koenig4, W. Koenig4, B. W. Kolb4,
R. Kotte5, F. Krizek15, R. Kr¨ ucken12, W. K¨ uhn8, A. Kugler15, A. Kurepin10, S. Lang4, J. S. Lange8, K. Lapidus11,E,
T. Liu14, L. Lopes2, M. Lorenz7,∗, L. Maier12, A. Mangiarotti2, J. Markert7, V. Metag8, B. Michalska3, J. Michel7,
D. Mishra8, E. Morini` ere14, J. Mousa13, C. M¨ untz7, L. Naumann5, J. Otwinowski3, Y. C. Pachmayer7, M. Palka7,
Y. Parpottas13, V. Pechenov4, O. Pechenova7, T. P´ erez Cavalcanti8, J. Pietraszko7, W. Przygoda3, B. Ramstein14,
A. Reshetin10, M. Roy-Stephan14, A. Rustamov4, A. Sadovsky10, B. Sailer12, P. Salabura3, A. Schmah11,F,∗,
E. Schwab4, J. Siebenson11, Yu.G. Sobolev15, S. Spataro8,D, B. Spruck8, H. Str¨ obele7, J. Stroth7,4, C. Sturm4,
A. Tarantola7, K. Teilab7, P. Tlusty15, M. Traxler4, R. Trebacz3, H. Tsertos13, V. Wagner15, M. Weber12,
C. Wendisch5, M. Wisniowski3, T. Wojcik3, J. W¨ ustenfeld5, S. Yurevich4, Y. Zanevsky6, P. Zhou5, P. Zumbruch4
(HADES collaboration)
1Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali del Sud, 95125 Catania, Italy
2LIP-Laborat´ orio de Instrumenta¸ c˜ ao e F´ ısica Experimental de Part´ ıculas , 3004-516 Coimbra, Portugal
3Smoluchowski Institute of Physics, Jagiellonian University of Cracow, 30-059 Krak´ ow, Poland
4GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany
5Institut f¨ ur Strahlenphysik, Forschungszentrum Dresden-Rossendorf, 01314 Dresden, Germany
6Joint Institute of Nuclear Research, 141980 Dubna, Russia
7Institut f¨ ur Kernphysik, Goethe-Universit¨ at, 60438 Frankfurt, Germany
8II.Physikalisches Institut, Justus Liebig Universit¨ at Giessen, 35392 Giessen, Germany
9Istituto Nazionale di Fisica Nucleare, Sezione di Milano, 20133 Milano, Italy
10Institute for Nuclear Research, Russian Academy of Science, 117312 Moscow, Russia
11Excellence Cluster ’Origin and Structure of the Universe’ , 85478 Munich, Germany
12Physik Department E12, Technische Universit¨ at M¨ unchen, 85748 M¨ unchen, Germany
13Department of Physics, University of Cyprus, 1678 Nicosia, Cyprus
14Institut de Physique Nucl´ eaire (UMR 8608), CNRS/IN2P3 - Universit´ e Paris Sud, F-91406 Orsay Cedex, France
15Nuclear Physics Institute, Academy of Sciences of Czech Republic, 25068 Rez, Czech Republic
16Departamento de F´ ısica de Part´ ıculas, Univ. de Santiago de Compostela, 15706 Santiago de Compostela, Spain
17Instituto de F´ ısica Corpuscular, Universidad de Valencia-CSIC, 46971 Valencia, Spain
Aalso at ISEC Coimbra, Coimbra, Portugal
Balso at Technische Universit¨ at Dresden, 01062 Dresden, Germany
Calso at Dipartimento di Fisica, Universit` a di Milano, 20133 Milano, Italy
Dalso at Dipartimento di Fisica Generale, Universita’ di Torino, 10125 Torino, Italy
Ealso at Institute for Nuclear Research, Russian Academy of Science, 117312 Moscow, Russia
Falso at Lawrence Berkeley National Lab, Berkeley California 94720, United States
∗corresponding author: Lorenz@Physik.uni-frankfurt.de, aschmah@lbl.gov
†deceased
Received: 28.09.2010 / Revised version: date
Abstract. We present transverse momentum spectra, rapidity distribution and multiplicity of Λ-hyperons
measured with the HADES spectrometer in the reaction Ar(1.76A GeV)+KCl. The yield of Ξ−is calculated
from our previously reported Ξ−/(Λ + Σ0) ratio and compared to other strange particle multiplicities.
Employing a strangeness balance equation the multiplicities of the yet unmeasured Σ±hyperons can be
estimated. Finally a statistical hadronization model is used to fit the yields of π−, K+, K0
Ξ−. The resulting chemical freeze-out temperature of T = (76 ± 2) MeV is compared to the measured
slope parameters obtained from fits to the transverse mass distributions of the particles.
s, K−, φ, Λ and
PACS.
25.75.-q, 25.75.Dw

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2 The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV
1 Introduction
Strange hadrons are particularly suitable probes of the
high density phase of nuclear matter produced in few GeV
heavy ion collisions. For instance, from systematic inves-
tigations of subthreshold K+production tight constraints
could be put on the nuclear equation of state at mat-
ter densities of 2-3 ρ0 [1,2,3]. Furthermore, kaon phase
space distributions and flow patterns are considered to
be sensitive to the in-medium kaon potential [4,5,6]. On
the other hand, due to strangeness conservation in the
strong interaction, kaon production is intimately linked
to the concurrent production of hyperons. While strange
particle production is well understood in elementary NN
collisions, in heavy ion reactions multi-step processes in-
volving mesons or baryon resonances open up many ad-
ditional production channels, even below threshold. Thus,
strangeness-exchange channels like πΛ → NK−have been
proposed to explain the observed K−yields [7], just as
feeding through the φ → K+K−decay has been [8].
Various aspects of strangeness production at SIS (Schw-
erionen Synchrotronat GSI Darmstadt) energies have been
investigated by the FOPI and KaoS experiments (for re-
views see [9,10]). Evidently, any in-depth understanding of
strangeness production and propagation in heavy ion re-
actions requires information on all particles with open or
hidden strangeness. The HADES collaboration has done a
complete measurement in the system Ar+KCl at a bom-
barding energy of 1.76A GeV. Results on kaon production
- i.e. K0
and φ-meson production in [8] and on the first observa-
tion at such a low beam energy of the double-strange Ξ−
hyperon in [12]. To complete the picture, hyperon produc-
tion remains to be addressed and this is the purpose of the
present paper. We report here on the results obtained with
the HADES detector on Λ production, from which, by ap-
plication of strangeness conservation, we could estimate
also the yield of the (not directly observed) Σ hyperons.
Furthermore, we compare our set of particle yields to the
result of a statistical hadronization model and discuss the
implications. Note that the FOPI collaboration performed
a similar analysis of strangeness production in the system
Ni+Ni at 1.93A GeV [13].
In Section 2 of this paper we give first a brief overview
of the HADES detector and relevant details of the Ar+KCl
data taking and then proceed to describe the employed
particle identification and Λ reconstruction procedures.
In section 3 we present spectra and production yields of
the Λ hyperons. The Λ result is used to extract the yield
of the double-strange Ξ−from our previously published
Ξ−/Λ ratio [12]. With all experimental yields established,
strangeness balance is applied to estimate the yield of the
unobserved charged Σ hyperons. In section 4, we discuss
all yields obtained in Ar+KCl with respect to a statisti-
cal hadronization model and confront the fitted chemical
freeze-out temperature with the measured slope parame-
ters obtained from transverse mass distributions. Finally
we summarize our findings in section 5.
s- have been published already in [11], on K+,K−
Fig. 1. Impact parameter distributions of all and LVL1 se-
lected Ar+KCl reactions obtained from the UrQMD transport
code [15].
2 Experimental setup and particle
identification
HADES is a charged-particle detector consisting of a 6-
coil toroidal magnet centered on the beam axis and six
identical detection sections located between the coils and
covering polar angles between 18◦and 85◦. Each sector is
equipped with a Ring-Imaging Cherenkov (RICH) detec-
tor followed by Multi-wire Drift Chambers (MDCs), two
in front of and two behind the magnetic field, as well as a
scintillator hodoscope (TOF/TOFino). Lepton identifica-
tion is provided mostly by the RICH and supplemented at
low polar angles with Pre-SHOWER chambers, mounted
at the back of the apparatus. Hadron identification, how-
ever, is based only on the time-of-flight and on energy-loss
information from TOF/TOFino, as well as from the MDC
tracking chambers. A detailed description of HADES is
given in [14].
For the present run an argon beam of ∼ 106parti-
cles/s was incident with a beam energy of 1.76A GeV on
a four-fold segmented KCl target with a total thickness
corresponding to 3.3 % interaction probability. A fast di-
amond start detector located upstream of the target was
intercepting the beam and was used to determine the in-
teraction time. The data readout was started by a first-
level trigger (LVL1) decision requiring a charged-particle
multiplicity, MUL ≥ 16, in the TOF/TOFino detectors.
Based on a full GEANT simulation of the detector re-
sponse to Ar+KCl events generated with the UrQMD
transport model [15], we determined that this LVL1 trig-
ger selected the 35% most central collisions with the mean
number of participating nucleons (?Apart?) equal 38.5 ±
3.9. Figure 1 illustrates the impact parameter distribu-
tions obtained from UrQMD calculations for two event
selections: none and according to the experimental LVL1
trigger condition.
The particle identification was done by a velocity vs.
momentum × polarity correlation, where the velocity was
determined by the time-of-flight measurement in the TOF
and TOFino scintillators with respect to the start sig-
nal and the tracked flight path. If needed, additional PID
power was gained from the energy-loss (dE/dx) informa-

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The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV3
tion in the MDC and scintillators. The particle identifi-
cation of kaons, φ, π−and Ξ−is described in [8,12,11].
Here we add only those details specific to the reconstruc-
tion of Λ hyperons in their decay channel Λ → p + π−
(B.R. = 63.9%, cτ=7.89 cm [16]). Note that at our beam
energies the reconstructed Λ yield contains also a contri-
bution from decays of the slightly heavier Σ0baryon into
a Λ and a photon.
The decay products of the Λ hyperons have been iden-
tified using the MDC dE/dx and time-of-flight informa-
tion. The topology of the Λ decay into p-π−pairs has
been used to suppress the combinatorial background of
uncorrelated pairs. Cuts on the distance between the pri-
mary event vertex and the decay vertex (dV 0), on the dis-
tances between the proton (dp), respectively the π−(dπ−)
track and the primary vertex, on the distance of closest
approach between the two tracks (ddca) and on the dis-
tance of the reconstructed mother particle trajectory to
the primary vertex (dpπ−) were applied. Furthermore, a
minimum opening angle (αpπ−) was required to guaran-
tee a good decay vertex resolution. All selections used for
the analysis are listed in Table I. For an estimation of the
systematic errors, the cut values have been varied within
reasonable limits. In total, 28 different cut combinations
were thus investigated, resulting in a total amount of re-
constructed Λ hyperons ranging from 36k to 191k.
Figure 2 shows the invariant-massspectrum of all proton-
π−pairs which passed the cuts listed in Table I. An event-
mixing technique has been used to model the combinato-
rial background of uncorrelated pairs. Displayed in Fig. 2
as a grey shaded histogram, the mixed event background
was normalized to the data on the left and right side of the
Λ peak. In total, for the optimal cut selection listed in Ta-
ble I about 100000 Λ hyperons were reconstructed, with a
mean signal-to-background ratio of 0.56. From a Gaussian
fit to the peak, the pole mass is determined to be 1114.3
MeV/c2, i.e. about 1.4 MeV/c2away from its listed value
[16]. We attribute this small difference to residual deficien-
cies of our track reconstruction and detector alignment.
3 Particle yields and strangeness conservation
3.1 Yields
For further kinematical studies the Λ signal has been de-
termined in nine rapidity bins, ranging from −0.75 <
yc.m. < +0.15 in steps of 0.1, and up to ten transverse
mass bins in steps of 50 MeV/c2. The background sub-
tracted signal yields were corrected for acceptance and re-
construction efficiency using a full GEANT simulation of
the detector system described in [11] and a track-embedding
method. The acceptance, which also includes the branch-
ing ratio of Λ → p+π−of 0.639, shows a smooth behavior
as a function of the transverse mass and varies for most
of the bins between 13% and 34%. The Λ reconstruction
efficiency is composed of the track reconstruction and par-
ticle identification efficiencies. The latter is dominated by
the cuts on the Λ decay topology and has values of 3% to
10%.
Fig. 2. Top: Invariant mass of all identified proton and π−
pairs after several cuts on the topology of the Λ decay kine-
matics were applied (see text for details). The grey shaded his-
togram shows the mixed-event combinatorial background, nor-
malized to the signal spectrum between 1080-1100 and 1130-
1150 MeV/c2. Bottom: Λ signal after background subtraction;
the solid red line shows a Gaussian fit to the signal.
The acceptance- and efficiency-corrected transverse-
mass spectra of Λ for the various rapidity bins are exhib-
ited in Fig. 3. Shown is the number of counts per LVL1
trigger, per transverse mass and per rapidity bin, divided
by m2
t. This representation is chosen in order to easily
apply Boltzmann fits to the resulting distributions, ac-
cording to
1
m2
t
d2M
dmtdycm
= C(ycm) exp
?
−(mt− m0)c2
TB(ycm)
?
.(1)
The solid lines in Fig. 3 show the results of Boltz-
mann fits, where TB(ycm) represents the inverse slope of
each distribution. The resulting TB(ycm) values are then
plotted in Fig. 4 as a function of the center-of-mass (cm)
rapidity (ycm= y −y(cm), where y(cm) = 0.858 for sym-
metric collisions at 1.76A GeV). The full symbols display
the measured data, whereas the open ones are the data

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4The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV
Table 1. Topological conditions values chosen for the Λ analysis (see text).
Cut
Value
dV 0
dp
dπ−
>dp
ddca
<10mm
dpπ−
<10mm
αpπ−
>14◦
>70mm>4.0mm
]
2
[MeV/c
Λ
-m
t
m
0200400
]
-3
)
2
)) [(MeV/c
c.m.
dy
M/(dm
2
) (d
2
(1/m
t
t
-15
10
-14
10
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
Λ
)
8
10
10
10
10
10
×
×
×
×
×
<+0.15 (
c.m.
<+0.05 (
c.m.
<-0.05 (
c.m.
<-0.15 (
c.m.
<-0.25 (
c.m.
+0.05<y
-0.05<y
-0.15<y
-0.25<y
-0.35<y
)
7
)
)
)
6
5
4
)
)
)
)
3
10
10
10
10
×
×
×
×
<-0.35 (
c.m.
<-0.45 (
c.m.
<-0.55 (
c.m.
<-0.65 (
c.m.
-0.45<y
-0.55<y
-0.65<y
-0.75<y
2
1
0
Fig. 3. Reduced (mt− mΛ) transverse mass spectra for dif-
ferent rapidity selections. For better legibility, the spectra are
scaled as indicated in the legend. The solid lines are fits with
Eq. 1 to the data.
reflected at c.m. rapidity. The error bars represent the
statistical errors. Assuming a thermal source, these tem-
peratures are expected to follow the relation
TB(ycm) =
Teff
cosh(ycm), (2)
yielding an effective temperature of Teff= (95.5 ±0.7(stat.)
+2.2(syst.)) MeV. Here the systematic error corresponds
to the variation of the cut values described above.
For each rapidity bin the transverse mass spectrum
was integrated in the following way: the yields in the cov-
ered bins were added and the fits were used to extrapo-
late into the unmeasured kinematic regions. The fits were
integrated from 0 to the first measured point and from
the last measured point to infinity. The fraction of the
extrapolated yield in the transverse mass spectra to the
total yield is 36-43% for the rapidity bins in the range
−0.65 < yc.m.< 0.15, and 65% for the rapidity interval
(−0.75 < yc.m. < −0.65). The results are shown in Fig.
5, where the obtained rapidity density distribution is dis-
c.m.
y
-101
[MeV]
B
T
0
20
40
60
80
100
120
Λ Λ
(measured)
(reflected)
Λ
Λ
0.7 MeV
±
= 95.5
eff
T
Fig. 4. Inverse-slope parameters from fits with Eq. (1) to the Λ
hyperon transverse mass spectra as a function of rapidity. The
solid line is a fit with Eq. (2) to the data points. The effective
temperature Teffis the function value at mid rapidity.
played. The full triangles show the values calculated by
the integration of the transverse mass spectra, while the
open triangles represent points reflected with respect to
the center-of-mass rapidity.
For the determination of the total Λ multiplicity per
LVL1 event, the measured spectra were integrated. The
extrapolation into the unmeasured region was done by fit-
ting either a gaussian or a linear function to the first four
data points, as shown in Fig. 5. The mean value of these
two different extrapolations is used for the total yield.
The fraction of the Gaussian extrapolation to the total
yield is about 4.2%, whereas the fraction of the linear ex-
trapolation is negligible. The inclusive total Λ multiplic-
ity per LVL1 event was found to be (4.09 ± 0.1(stat.) ±
0.17(extr.)+0.17
to the extrapolation uncertainty in mtand the third one
to the systematic error obtained from the cut variations.
A detailed description of the Λ analysis can be found
in [17]. With the yield of the Λ + Σ0hyperons known
one can now also quantify the production of the double-
strange Ξ−hyperon from the Ξ−/(Λ + Σ0) ratio [12] to
be (2.3 ± 0.9) × 10−4, adding statistical and systematical
errors quadratically. Note that this value is of the same
order of magnitude as the yield of the φ meson [8].
Table 2 summarizes all particle yields extrapolated to
full phase space as well as the corresponding inverse slope
parameters from fits to the particle mtspectra; results on
K+,K−,K0
s, and φ are taken from [8,11].
−0.37(syst.))×10−2, where the second error refers

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The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV5
Table 2. Multiplicities (i.e. yield/LVL1 event) and effective temperatures of particles produced in Ar+KCl reactions at 1.76A
GeV. The error on the Σ and Ξ−yield is the quadratically added statistical and systematic error.
Particle
π−
Λ + Σ0
K+
K0
K−
φ
Ξ−
Σ++ Σ−
Multiplicity
3.9 ± 0.1 ± 0.1
Teff [MeV]
82.4 ± 0.1+9.1
95.5 ± 0.7 + 2.2
89 ± 1 ± 2
92 ± 2
69 ± 2 ± 4
84 ± 8
-
-
Reference
[11]
this work
[8]
[11]
[8]
[8]
[12]
−4.6
(4.09 ± 0.1 ± 0.17+0.17
(2.8 ± 0.2 ± 0.1 ± 0.1) × 10−2
(1.15 ± 0.05 ± 0.09) × 10−2
(7.1 ± 1.5 ± 0.3 ± 0.1) × 10−4
(2.6 ± 0.7 ± 0.1 − 0.3) × 10−4
(2.3 ± 0.9) × 10−4
(0.75 ± 0.65) × 10−2
−0.37) × 10−2
S
estimated via strangeness balance
c.m.
y
-101
dM/dy
0
10
20
30
40
50
-3
10
×
Λ Λ
(measured)
(reflected)
Λ
Λ
Fig. 5. Rapidity distribution of Λ hyperons. The closed sym-
bols refer to measured data points calculated from the trans-
verse mass spectra, whereas the open symbols show the data
points reflected about center-of-mass rapidity. For the extrap-
olation to unmeasured rapidity values a linear and a Gaussian
function were fitted to the first four data points (see text).
3.2 Strangeness balance
The strong interaction conserves strangeness, i.e. the num-
bers of s and s quarks produced in a heavy ion reaction
must be equal. As those quarks are ultimately bound in
hadrons the multiplicities of strange particles fulfill a bal-
ance equation which can be written at SIS energies as:
K++ K0= Σ0±+ Λ + K−+¯K0+ 2Ξ0,−
(3)
where, for simplicity, the symbols denoting the particles
stand for their respective yields at the time of production.
Note that this equation takes care of the strong decay of
heavier strange resonances via the counting of their de-
cay products, namely kaons and Λs. As mentioned ear-
lier, the Σ0can not be separated from the Λ, thus this
contribution is to be counted explicitly together with Λs.
Analogously, according to our analysis procedure, most
Ξ−,0decay products feed the Λ channel and are counted
as Λs, when strictly speaking strangeness changing weak
decays are involved. (Note that anyhow the Ξ−,0contri-
butions are small.) In case of the neutral kaons, we mea-
sure in fact the yield of the K0
K0
K0)/2. Assuming isospin symmetry the yield
of the¯K0should be contributing here at the same order
as the K−yield. Eq. (3) can then be rewritten using the
measured yields. Hence the unobserved Σ±hyperon yield
can be estimated as:
s, which obeys the equality
s= (K0+¯
Σ++ Σ−= K++ 2K0
s− (Σ0+ Λ) − 2Ξ−− 3K−
(4)
Still heavier multi-strange particles, e.g. Ω hyperons,
have significantly higher production thresholds and should
not contribute sizeably at SIS energies. From Eq. (4) a
total multiplicity of charged Σ hyperons of (7.5 ± 6.5) ×
10−3is deduced when using the values of the multiplicities
listed in Tab. 2. The error is the quadratic sum of the
statistical and systematical error of the different yields.
The only other published multiplicity of charged Σ hy-
perons in heavy ion collisions, based on a similar analysis
of strangeness yields measured with the FOPI detector at
GSI in Ni+Ni reactions at 1.93A GeV, is (7±8)×10−3[13].
Differences with respect to our analysis are: (1) a higher
beam energy (1.93 vs. 1.76A GeV), (2) a larger reaction
system (58+58 vs. 40+37), and (3) a different centrality
selection (?Apart? = 71 vs. 38.5). In view of the higher
bombarding energy and larger system size, one would ex-
pect a larger charged Σ contribution.
4 Discussion
4.1 Comparison with statistical hadronization
Statistical hadronization models (SHM) have been suc-
cessful in fitting particle yields or yield ratios from rel-
ativistic and ultrarelativistic heavy ion collisions [18,19,
20,21]. With the help of SHM fits it has been possible
to reconstruct systematically the chemical freeze-out line
in the T – µb plane of the nuclear phase diagram with
µb being the baryochemical potential (see e.g. [21,22]).
However, while the various SHM approaches agree fairly

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6The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV
well at high bombarding energies, discrepancies appear
in the low-energy regime. Indeed, at the lower energies
it is not even clear, whether chemical equilibrium can be
reached [23] and therefore the question arises whether a
statistical treatment of particle production is meaning-
ful. The situation is further complicated by the need for
strangeness suppression, which is handled differently in
the various SHM implementations. Furthermore, at SIS
energies, many particles are produced subthreshold and
their yields remained poorly known. In the following we
fit eight particle yields obtained from our Ar+KCl run
with a statistical hadronization model.
We choose the freely available THERMUS code [24],
using the mixed canonical ensemble where strangeness is
exactly conserved while all other quantum numbers are
calculated grand canonically. We handle the strangeness
suppression by introducing a strangeness correlation ra-
dius Rc within strangeness has to be exactly conserved;
this is discussed in [25]. We fit simultaneously all parti-
cle yields except the Σ±listed in Table 2, as well as the
mean number of participants ?Apart? and constraining the
charge chemical potential µQusing the ratio of the baryon
and charge numbers of the collision system. We find the
chemical freeze-out at a temperature of Tchem= (76 ± 2)
MeV and at a baryochemical potential of µb= (799±22)
MeV. The strangeness correlation radius comes out as
Rc = (2.2 ± 0.2) fm, which corresponds to about half
the fitted radius R = (4.1 ± 0.5) fm of the whole fire-
ball. The exclusion of the Ξ−from the fit changes the
parameters only on the percent level, but the χ2/d.o.f.
value of the fit improves from 13.9/4 to 7.8/3. Fig. 6 shows
the resulting freeze-out point together with a compilation
of similar points [26,21,27] in the T – µb plane. Our re-
sult, as well as the FOPI result from the collision system
Al+Al at 1.9A GeV, differ from the regularity of freeze-
out points following the fixed energy per particle condition
?E?/?N? ≈ 1 GeV, which is one of the commonly proposed
freeze-out criteria [21]. This might be due to the light col-
lision systems, since small systems have the tendency to
show higher freeze-out temperatures.
A detailed comparison of the data with the statistical
model fit is shown in the upper part of Fig. 7, while the
lower part of this figure depicts the ratio of data and fit.
All particles with strangeness S=1 are well described.
A particularly interesting case is the φ meson. The φ
is treated as a strangeness neutral object in the Rc for-
malism and is therefore not suppressed at all. Its yield is
well described by the SHM. This means that the φ yield
is compatible with the assumption that it takes part in
the equilibration of the hadrons. This is quite different
from the situation at higher bombarding energies, where
the φ requires indeed an effective strangeness between 1
and 2 to have the appropriate suppression in the SHM
and to reproduce the data [25]. For an understanding of
φ production, one may have a look at the φ/K−ratio
which, according to the SHM with Rc, should rise at low
beam energy. Such a behavior is indeed supported by our
data, as already discussed in [8], and the ratio seems to
approach the value seen in elementary NN reactions [28].
[MeV]
b
µ
02004006008001000 1200
T [MeV]
0
50
100
150
200
RHIC/SPS/AGS (a)
RHIC/SPS/AGS/SIS (b)
HADES (Ar+KCl)
FOPI (Al+Al)
Fig. 6. (Color online) Chemical freeze-out points in the T –
µb plane. The filled black circles (a) are taken from [26], the
black open triangles (b) are from [21]. The red circle is taken
from [27]. The THERMUS fit to our Ar+KCl data is shown
as blue triangle. The dashed line correponds to a fixed energy
per nucleon of 1 GeV, calculated according to [21].
yield
-5
10
-3
10
-1
10
10
2
10
=2.61 GeV
NN
s
√
Data,
2.1MeV,
±
T=75.8
0.2fm, R
±
=2.2
C
R
21.6MeV,
0.5fm
±
=799.4
±
=4.1
b
µ
V
Exp/THERMUS
0
0.5
1
1.5
part
A
-πΛ
+
K
s
0
K
-
K φ
-
Ξ
+-
Σ
9
±
24
Fig. 7. (Color online) The upper plot shows the yields of sec-
ondary hadrons in Ar+KCl reactions (filled red circles) and
the corresponding THERMUS fit (blue bars). The lower plot
shows the ratio of the experimental value and the SHM value.
For the Ξ−the ratio number is quoted instead of a point.

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The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV7
Then one is left with the question: Are the observed φ
produced like in elementary collisions or is it just by coin-
cidence, and different production mechanisms have to be
considered [29]?
According to the strangeness suppression mechanism
implemented in SHM, the double-strange Ξ−(S=2) should
be suppressed strongly with respect to the φ with its hid-
den strangeness (S=0). Nevertheless, our measured Ξ−
yield is of the same magnitude as the one of the φ, i.e. the
data show no indication for any strangeness suppression.
This is very surprising since the Ξ−yields observed above
threshold at RHIC [30], at SPS [31] and even at AGS [32]
are consistent with statistical model fits. In fact the same
secondary pion-hyperon process π + Y → φ + Y , which
was invoked by Kolomeitsev and Tomasik [29] to explain
the enhanced φ yield, can here be the origin of the high
Ξ production via the reaction π + Y → Ξ + K.
To get a better understanding, we may have to move
away from the SHM. One may calculate the probability
for the production of two ss pairs in one collision. As-
suming that both pairs are independently created, their
production probability P2ssis given as the square of the
single-pair production probability Pss. Keeping associated
production in mind, Psscan be estimated as the combined
multiplicity of all particles that carry a strange quark,
respectively the combined multiplicity of all anti-strange
particles, i.e. K++K0+φ, yielding Pss≃ 0.05 and hence
P2ss≃ 0.0025. Considering that the observed Ξ−yield is
in fact an order of magnitude smaller, we conclude that
in 10% of these events both s quarks end up together in
a Ξ−, whereas from strangeness suppression in the SHM
one obtains less than 1%.
A different realization of the SHM using the grand-
canonical ensemble and γsfor strangeness suppression de-
livers comparable freeze-out parameters, with Tchem =
(77 ± 5) MeV, µb = (806 ± 26) MeV, R = (3.9 ± 0.5)
fm and γs= 0.08±0.01 but fails to reproduce the φ mul-
tiplicity by two orders of magnitude due to its suppression
with γ2
s.
4.2 Chemical vs. kinetic freeze-out
The temperature Tchemobtained for the chemical freeze-
out can be compared with the inverse-slope parameter
Teffobtained from Boltzmann fits to the mtspectra of the
different particle species. Apparently most of the inverse-
slope parameters are higher than the chemical freeze-out
temperature of the system. A pure Boltzmann shape can
be distorted by various effects, like collective motion or
early vs. late particle decays. One example is apparent in
the difference between the K+/K0
Fig. 8). The much lower value of Teffof the K−has often
been interpreted as due to its much later freeze-out time
[9]. In another possible scenario, the slope is affected by
the admixture of soft K−stemming from φ decays [33].
Effects of collective flow, on the other hand, should influ-
ence the transverse mass slope the more, the higher the
particle mass is. From Fig. 8, where the fitted tempera-
tures are ordered by increasing particle mass, this seems
sand K−slopes (see
Fig. 8. (Color online) Effective temperature Teff of all mea-
sured particle species as a function of their mass. The horizon-
tal line and error band show the chemical freeze-out tempera-
ture Tchem from the THERMUS fit.
not to be a strong effect as expected for a small collision
system like Ar+KCl. However the inverse-slope parameter
seems to be slightly decreasing with decreasing mass.
While statistical hadronization models are able to de-
scribe particle multiplicities with good agreement they are
unable to reproduce their phasespace distributions.Transport
models on the other hand are able to describe kaon and
hyperon yields, as well as kinematical observables with
good agreement since many years. While recent calcula-
tions are able to describe also the φ yield [34], the high Ξ
yield remains unexplained by transport up to know.
5 Summary and conclusions
We have presented phase space distributions of Λ hyper-
ons in Ar+KCl at 1.76A GeV measured with the HADES
spectrometer at GSI. Combining the measured Λ + Σ0
yield with our former data on strangeness production in
this system we have estimated the yield of the double-
strange Ξ−hyperon. We find that it is of the same order of
magnitude as the one of the φ meson. The fraction of the
unobserved charged Σ±hyperons could be constructed
using strangeness conservation.
Applying to these hadron yields a statistical model fit
we find that we are able to describe all measured parti-
cle yields with fair agreement except for the Ξ−, which
is doubly suppressed in our statistical approach. The φ,
however, is well reproduced without any suppression, in
sharp contrast to the situation at higher energies, where
a suppression is observed.
The HADES collaboration gratefully acknowledges the
support by BMBF grant 06MT9156, 06GI146I,06FY171
and 06DR9059D (Germany), by GSI (TMKrue 1012, GI
/ME3, OF/STR), by Excellence Cluster Universe (Ger-
many), by grants GA AS CR IAA100480803 and MSMT
LC 07050 MSMT (Czech Republic), by grant KBN5P03B
140 20 (Poland), by INFN (Italy), by CNRS/IN2P3 (France),

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8 The HADES collaboration (G. Agakishiev et al.): Hyperon production in Ar+KCl collisions at 1.76A GeV
by grants MCYT FPA2000-2041-C02-02and XUGA PGID
FPA2009-12931T02PXIC20605PN(Spain), by grant UCY-
10.3.11.12(Cyprus), by INTAS grant 06-1000012-8861and
EU contract RII3-CT-506078.
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