Production of K+ and of K- Mesons in Heavy-Ion Collisions from 0.6 to 2.0 AGeV Incident Energy

0.82 MB·English

by  A. Foerster

version of February 8, 2008
Production of K+ and of K− Mesons in Heavy-Ion Collisions
from 0.6 to 2.0 A GeV Incident Energy
A. F¨orsterb,∗, F. Uhligb,a, I. B¨ottcherd, D. Brilla, M. De¸bowskie,f, F. Dohrmannf, E. Grossef,g,
P. Koczon´a, B. Kohlmeyerd, S. Langb,a, F. Lauea,+, M. Manga, M. Menzeld, C. Mu¨ntzb,a,c, L. Naumannf,
H. Oeschlerb, M. P loskon´a,c, W. Scheinastf, A. Schmahb,a, T. J. Schuckc,∗, E. Schwaba, P. Sengera,
Y. Shinc, J. Speera,†, H. Stro¨belec, C. Sturmb,a,c, G. Sur´owkaa,e, A. Wagnerf,b, W. Walu´se
(KaoS Collaboration)
a Gesellschaft fu¨r Schwerionenforschung, D-64220 Darmstadt, Germany
b Technische Universit¨at Darmstadt, D-64289 Darmstadt, Germany
c Johann Wolfgang Goethe-Universit¨at, D-60325 Frankfurt am Main, Germany
d Phillips-Universit¨at, D-35037 Marburg, Germany
7
0 e Uniwersytet Jagiellon´ski, PL-30059 Krak´ow, Poland
0 f Forschungszentrum Dresden-Rossendorf, D-01314 Dresden, Germany
2 g Technische Universit¨at Dresden, D-01062 Dresden, Germany

n ∗ Present address: Max-Planck-Institut fu¨r Kernphysik, D-69117 Heidelberg, Germany
a + Present address: Brookhaven National Laboratory, Upton, NY 11973, USA
J
† deceased
8
This paper summarizes the yields and the emission patterns of K+ and of K− mesons measured
1
in inclusive C+C, Ni+Ni and Au+Aucollisions at incident energies from 0.6 A GeV to 2.0 A GeV
v
using the Kaon Spectrometer KaoS at GSI. For Ni+Ni collisions at 1.5 and at 1.93 A GeV as well
4
asforAu+Auat 1.5A GeVdetailed resultsof themultiplicities, oftheinverseslopeparameters of
1
theenergydistributionsandoftheanisotropiesintheangularemissionpatternsasafunctionofthe
0
collisioncentralityarepresented. Whencomparingtransport-modelcalculationstothemeasuredK+
1
production yields an agreement is only obtained for a soft nuclear equation of state (compression
0
7 modulus KN ≈ 200 MeV). The production of K− mesons at energies around 1 to 2 A GeV is
0 dominated by the strangeness-exchange reaction K−N⇀↽πY (Y=Λ,Σ) which leads to a coupling
/ betweentheK− andtheK+ yields. However,bothparticlespeciesshowdistinctdifferencesintheir
x emission patternssuggesting different freeze-out conditions for K+ and for K− mesons.
e
-
l PACSnumbers: 25.75.Dw
c
u
n
I. INTRODUCTION reactions at these incident energies is the accumulation
:
v ofthe necessaryenergybymultiple collisionsofparticles
i inside the reaction zone. Higher densities increase the
X Relativistic heavy-ion collisions at incident energies
number of these collisions and especially second genera-
r rangingfrom0.6to2.0AGeVprovideauniqueopportu-
a tion collisionslike ∆N with sufficiently high relative mo-
nitytostudythebehaviorofnuclearmatterathighden-
mentumtocreateaK+ occurmostfrequentlyduringthe
sities. These studies are important challenges for testing
high-density phase of the reaction. The density reached
thepresentunderstandingofnuclearmatter. Inaddition,
in the reaction zone depends on the stiffness of nuclear
theyareofrelevanceforastrophysics,asthemodellingof
matter. Because of their specific production mechanism
neutronstarsorofsupernovaedependsontheproperties
and because of their rather long mean free path (≈5 fm
of nuclear matter under these extreme conditions [1].
at normal nuclear density) K+ mesons are ideal probes
In central Au+Au collisions at the incident energies toexplorethe high-densityphaseofaheavy-ionreaction
under investigation densities of 2 – 3 times normal nu- andtostudythestiffnessofthenuclearequationofstate
clear matter density can be reached[2, 3, 4]. A sensitive (EoS) [5, 6, 7, 8, 9].
probetotesttheseconditionsistheproductionofstrange In contrast, the behavior of K− mesons in a dense nu-
mesons at or below the production thresholds of these clear medium is expected to be very different from the
particles in free NN collisions. The rest mass of charged one of the K+ mesons due to two distinct properties:
kaonsis0.454GeV.FortheK+ productionthethreshold (i) The interaction with nuclear matter: The K+ are
in NN collisions is 1.58 GeV (in the laboratory system)
hardly absorbed in nuclear matter due to strangeness
asdefinedbytheassociateproductionNN→K+ΛNand conservation. It is very unlikely that a rare K+ (con-
it is 2.5 GeV for the K− production via pair creation
taining an s¯ quark) encounters an equally rare hyperon
NN→NNK−K+. Y (Λ, Σ) containing an s quark. The K− on the con-
ThekeymechanismfortheK+productioninheavy-ion trary, can easily be absorbed on a nucleon converting it
2
into a hyperon and a pion. Consequently, the mean free II. THE EXPERIMENT
path of the K− is significantly shorter than the one of
the K+. The strangeness-exchangereaction K−N⇀↽πY A. The Setup
has a large cross section and is therefore responsible for
the appearance and disappearance of K− mesons. This
The experiments wereperformed with the KaonSpec-
channel has been suggested to be the dominant produc-
trometer(KaoS)atthe heavy-ionacceleratorSIS(Schw-
tion mechanism in nucleus-nucleus collisions [5] and this
erionensynchrotron) at the GSI (Gesellschaft fu¨r Schw-
has been demonstrated in [10, 11, 12].
erionenforschung) in Darmstadt, Germany. A detailed
(ii) The influence ofKNpotentials: Accordingtovari- description is presented in [32]. Here we just briefly re-
oustheoreticalapproachestheKNinteractionisgoverned view the main features.
by the superposition of a scalar and a vector potential
Thesetupofthequadrupole-dipolespectrometerKaoS
[13, 14, 15, 16, 17, 18]. While the scalar potential acts
isshowninFig.1. Positivelyandnegativelychargedpar-
attractivelyonbothkaonspecies,thevectorpotentialre-
ticles are measured separately using different magnetic
pelsK+andattractsK−. ForK+thesetwocontributions
field polarities. The magnetic spectrometer has an ac-
almost cancel leading to a small repulsive K+N interac-
ceptance in solid angle of Ω ≈ 30 msr and covers a mo-
tion. For the K− the addition of both attractive interac-
mentum bite of p /p ≈ 2. The short distance of 5
max min
tions results ina stronglyattractivepotential. Attempts
- 6.5 m from the target to the focal plane minimizes the
toobservetheseeffectsintherespectiveproductioncross
numberofkaondecaysinflight. The lossofkaonsbyde-
sections are under discussion [12, 19, 20, 21, 22, 23, 24].
cay and due to the geometrical acceptance is accounted
These potentials are predicted to have a sizeable effect
for by corrections which are determined by Monte-Carlo
onthe azimuthalemissionpatternsofK+ andofK− (el-
simulations using the code GEANT [33]. Particle iden-
liptic flow)[25,26]whichhasbeen observedatthe Kaon
tification is based on momentum and on time-of-flight
Spectrometer [27, 28].
(TOF) measurements. The trigger system is as well
This paper intends to give a comprehensive overview basedonthetime-of-flightinformationtoseparatepions,
on the cross sections and on the emission patterns of kaonsandprotons. Fortheseparationofhighmomentum
the K+ and of the K− production in mass-symmetric protons from kaons a threshold Cherenkov detector [34]
heavy-ion reactions in the incident energy range from is used in addition. The trigger system suppresses pions
0.6 to 2 A GeV. It summarizes new as well as previ- and protons by factors of 102 and of 103, respectively.
ously published [7, 10, 19, 20, 29] results on inclusive In total there are three time measurements using seg-
collisions of Au+Au, Ni+Ni and C+C collisions. Fur- mentedplastic scintillatorarrays: The TOFStartdetec-
thermore, new results focussing on the centrality depen- torbetweenthequadrupoleandthedipole(16modules),
dence of Ni+Ni collisions at 1.5 and at 1.93 A GeV and the TOF Stop detector in the focal plane of the spec-
of Au+Au collisions at 1.5 A GeV are presented. Re- trometer (30 modules), and the Large-Angle Hodoscope
sultsonthekaonproductioninthemass-asymmetriccol- (LAH)aroundthetargetpointcoveringpolarlaboratory
lisionsystemsC+AuandAu+C havebeenpublishedre- angles of 12◦ ≤ θ ≤ 48◦ (84 modules). The latter
lab
cently[30]. Theresultsonthe azimuthaldistributionsof allows for a second time-of-flight measurement for back-
kaons[27,28]aswellasofpionsandofprotons[31]have ground rejection and for the determination of the col-
beenpublishedandfurtherpublicationsonthistopicare lision centrality using the number of measured charged
in preparation as well as a review on pion production. particles.
Thispaperisstructuredinthefollowingway: First,in The trajectory reconstruction is based on three large-
SectionII,adescriptionoftheexperimentalsetupandof area Multi-Wire Proportional Counters (MWPC 1 -
thedataanalysisisgiven. InSectionIIIAwesummarize 3) [35], one between the quadrupole and the dipole and
the results on cross sections, energy distributions, and two behind the dipole magnet, each of them measuring
polarangledistributionsforinclusivecollisions,i.e.with- two spatial coordinates. The efficiencies for kaon detec-
out any selectionin the collisioncentrality. Section IIIB tion are larger than 95% for each of these detectors.
presents a detailed study of the centrality dependence of The beam intensity is monitoredusing twoscintillator
the K+ and of the K− production. In Section IVA the telescopespositionedatbackwardangles(θ =±110◦),
lab
measured yields of K+ and of K− mesons are discussed measuring the flux of charged particles produced in the
showing that their production is correlated. Despite this target which is proportional to the beam intensity. The
correlationoftheproductionyieldstheemissionpatterns absolute normalization is obtained in separate measure-
ofK+ andofK− mesonsdiffersignificantly. SectionIVB mentsatlowbeamintensitiesusingaplasticscintillation
discusses these differences with respect to the influences detector directly in the beam line. The beam intensities
of the KN-potentials and with respect to different emis- have been chosen such, that the efficiency of the data
siontimesofthetwokaonspecies. SectionIVCcompares acquisition system (DAQ) due to dead time was always
the production yields of K+ mesons in different collision above 50%.
systemstorecenttransportmodelcalculationstoextract The spectrometeris mountedonaplatformwhichcan
information on the stiffness of the nuclear equation of be rotated around the target point on an air cushion in
state. a polar angel range from θ =0◦ to 130◦. The angular
lab
3
]
c E = 1.0 AGeV
/ beam
V 70o
e 1 54o
G
[ 84o 44o

t
p
0.5
1 m
0
E = 1.5 AGeV
FIG. 1: Top view of the Kaon Spectrometer KaoS with its beam
various detector components. 60o
1 48o
target thickness[mm] interact. prob. 72o 40o
C 3.0 2.7% 32o
Ni 0.8 2.1%
0.5
Au (0.6,1.0,1.135 A GeV) 1.0 3.6%
Au(0.8,1.5 A GeV) 0.5 1.8%
0
TABLE I: Thicknesses and interaction probabilities for the
E = 1.93 AGeV
targets used in thevarious experiments. beam
1 50o
orauntgtehcisovpearpeedrawteeawcihllpaolwsiatyiosnqiuso∆teθltahbe=m±ea4n◦.vaTluhero.uTghhe- 60o 40o
32o
momentumcoverageismaximizedbymeasuringdifferent
magnetic field settings (|Bdipole| = 0.6, 0.9, and 1.4 T). 0.5
Theresultingcoverageforkaonsinrapiditynormalizedto
the beam rapidity y/y and in transversemomentum
beam
p is sketched in Fig. 2 for three different beam energies
t
(1.0,1.5,and1.93AGeV).Theshadedareascorrespond 0
to different angular settings θ of the spectrometer in 0 0.5 1
lab
the laboratory as denoted in the figure and to various y/y
beam
magnetic field settings.
In this paper we report on measurements of the colli-
sion systems C+C (0.8, 1.0,1.2, 1.5, 1.8,and 2.0 A GeV FIG.2: (Coloronline)ExamplesforthecoverageoftheKaon
beam energy), Ni+Ni (1.1, 1.5, and 1.93 A GeV), and Spectrometer in transverse momentum pt and in normalized
Au+Au (0.6, 0.8, 1.0, 1.135, and 1.5 A GeV). The tar- rapidity y/ybeam for several laboratory angles θlab (as indi-
gets as well as their respective thicknesses and interac- cated) and for various magnetic field settings at 1.0 A GeV,
tionprobabilitiesaregiveninTableI. Due tothe energy at 1.5 A GeV,and at 1.93 A GeV incident energy.
lossintheAutargetstheaverageeffectivebeamenergies
Eeff for kaon production in these cases are 0.56, 0.78,
beam ing)andfinallyre-injectionintotheSISandacceleration
0.96,1.1,and1.48AGeV.Fortheothertargetmaterials
up to 1.5 A GeV.
the energylossisnegligible. Throughoutthe textwe use
thevaluesofthenominalbeamenergiesE . However,
beam
in all figures displaying data as a function of the beam
energy the data points are plotted at Eeff . B. Data Analysis
beam
In the case of the 1.5 A GeV Au beam an exceptional
operationoftheGSIacceleratorfacilitywasrequired: ac- 1. Track Reconstruction
celeration of 197Au63+ ions with the synchrotron SIS up
toanenergyof0.3AGeV,thenextractionandfullstrip- For the reconstruction of particle tracks in the spec-
ping,followedbyinjectionintotheExperimentalStorage trometer,reconstructionfunctionscorrelatingthespatial
Ring (ESR) where the beam was cooled (electron cool- coordinates measured by different detectors are used to
4
combine the information of different detectors to track
cisanudseiddattoes.calFcuolrateexathmepxle-,cooonredinreactoenisntrtuhcetioMnWfuPnCctbioen- yield10 7 ND pi+laNb=i,0 1.2.16A7-G0.e5V0,7 q Glaeb=V4/c0o
6 p
tweenthequadrupoleandthedipole(x1)asafunctionof 10 p +
the x-coordinates of the two MWPCs behind the dipole
5
(x ,x ). By comparing a measured position in one de- 10 w/o
2 3
TOF-
tector with the calculated position based on the hits in Trigger
4
other detectors using the reconstruction functions, track 10 K+
candidatesarecreated. This is done forthe spatialcoor-
3
dinates in the MWPCs as well as for the assignment of 10
the modules of the TOF detectors. with TOF-Trigger
2
10
The reconstruction functions are determined by
Monte-Carlosimulations using a complete descriptionof
10 with TOF-Trigger
theexperimentalsetupwithinGEANT.Singletracksare and Cuts
followed through the spectrometer and the correlation
1
fuupncttoiosnesveanrtehdoertderemr ianneddwbyithfitutipngtopothlyrneeomxi-acloofurndcintiaotness 10 7 ND pi+N=i,0 1.4.9030A-0G.7e6V0, Gq leaVb=/c40o
and up to three y-coordinates to all these simulated 6 lab
tracks. 10 p + p
After the reconstruction a resulting track candidate 5
10
consistsofx-andy-coordinatesinallthethreeMWPCs,
the module numbers, the time and the energy-lossinfor- 4
mation of the TOF Start and of the TOF Stop detector 10 K+
as well as the time and the multiplicity information of 3
10
the Large Angle Hodoscope.
To determine the efficiency of the tracking procedure 10 2
GEANTisused. Thistimenotonlysingletracksaregen-
erated but combinations of one or severaltracks and ad- 10
ditional backgroundhits in the different detectors as ob-
served in the experiment. The resulting efficiencies vary 1
with the laboratory angle, the magnetic field strength, 10 6 Ni+Ni, 1.93AGeV, q lab=40o
and the size of the collision system because of varying D p =0.400-0.760 GeV/c
lab
track and background multiplicities. The resulting effi- 5 p -
10
ciencies of the tracking procedure are always largerthan
90%.
4
For each track candidate constructed in the preceding 10
steps, the momentum p and the length of the flight
lab
3
path ∆l between the TOF Start and the TOF Stop de- 10
tector modules are obtained from a lookup table gener- K-
ated with GEANT. From these quantities together with 10 2
the measured time difference ∆t between the two TOF
detectors, the squared mass over charge ratio (m/Z)2 is
10
calculated using
m 2 p ·c 2 ∆t·c 2 1
lab 0 0.2 0.4 0.6 0.8 1
= −1 . (1)
(cid:16)Z(cid:17) (cid:16) Z (cid:17) "(cid:18) ∆l (cid:19) # (m/Z)2 [(GeV/c2)2]
Since the particles under investigation have Z = 1 we
simply use ’mass’ in the following.
FIG. 3: (Color online) Distributions of the squares of the
masses assigned to the reconstructed tracks in three differ-
ent cases: Ni+Ni collisions at 1.1 A GeV (upper panel), at
2. Background Reduction and Cross Section Calculation
1.93 A GeV (middle panel), both using the field polarity for
positivelychargedparticles,andat1.93AGeVfornegatively
Figure 3 shows mass distributions for Ni+Ni collisions chargedparticles(lowerpanel). Differentlyshadedareasshow
at θlab = 40◦. The distribution in the upper panel has the impact of the TOF trigger and of the application of the
been measured at a beam energy of 1.1 A GeV and at selection criteria duringthedata analysis. Details see text.
particle momenta p =0.267 − 0.507 GeV/c using the
lab
magnetic fieldsetting for positivelychargedparticles. In
5
thiscaseoflowbeamenergyandoflowparticlemomenta
theregionofthekaonmassisdominatedbybackground. d
1000 p =0.40-0.75 GeV/c p =0.40-0.45 GeV/c
The distribution labelled “w/o TOF-Trigger” was mea- el lab 100 lab
i
sured using trigger conditions that forced every particle y
passing through the spectrometer to be recorded. The
distributionlabelled“withTOF-Trigger”showstheclear 500
50
reduction of pions and protons being recorded when us-
ing the time-of-flight trigger,but still no clear K+ signal
canbeseen. Thesituationisdifferentathigherbeamen-
0 0
ergiesorathigherparticlemomentawherethekaonsare
0.4 0.5 0.6 0.4 0.5 0.6
clearly visible already in the distributions “with TOF-
Trigger”ascanbe seenin the twolowerpanelsofFig.3.
p =0.55-0.60 GeV/c p =0.70-0.75 GeV/c
They show mass distributions for Ni+Ni at 1.93 A GeV 200 lab lab
50
for positively charged particles in the middle panel and
for negatively charged particles in the lower panel. In
the lattercase,the triggercondition“w/oTOF-Trigger”
was not measured. 100 25
To reduce the remaining background effectively with-
outloosingtoomanykaonstwotypesofselectioncriteria
0 0
are applied:
0.4 0.5 0.6 0.4 0.5 0.6
(i) The so-called “geometrical cuts”: These selection
m/Z [GeV/c2]
criteria are based on the comparison between measured
positions in one of the MWPCs and those extrapolated
fromhits in the other twousing the reconstructionfunc- FIG.4: (Coloronline)MassdistributionsforNi+Nicollisions
tions described in the previous section. These selection at 1.1 A GeV at θlab =40◦ for different particle momenta as
criteriaareadjustedusingmeasurementsduringthesame indicated. The solid lines depict the results of a combined
experiment which are nearly free of background(highest fit to the background and to the peak at the kaon mass, the
dashed lines show thebackground part only.
beam energy and/or largest laboratory angle). This can
be done since the particle trajectories inside the spec-
trometer only depend on the magnetic field andthe geo-
mass distributions for Ni+Ni collisions at 1.1 A GeV at
metrical setup but not on quantities like θ or E .
lab beam θ = 40◦ as an example with a significant background
lab
(ii) The so-called “velocity cut”: For each track can-
contamination. The fits are performed separately for
didate the particle velocity between the TOF Start de-
each bin in particle momentum (in most cases having a
tector and the TOF Stop detector is calculated as well
widthof0.05GeV/c),theupperleftgraphshowsthedis-
as the velocity between the Large-Angle Hodoscope and
tributionintegratedoverthefullmomentumrangeofthis
theTOFStopdetector. Thecomparisonofthesetwove-
particularmagneticfieldsetting forillustrationpurposes
locitiesisapowerfultooltosuppressbackgroundcreated
only. The solidlinesdepictthe resultofthe combinedfit
by fake track candidates. The “velocity cut” is adjusted
tothebackgroundandtothepeakatthe kaonmass,the
using the measurements nearly free of background as in
dashed lines show the background part only.
the case of the “geometrical cuts”.
The cross sections are calculated from the number of
Dependingontheinitialsignal-to-backgroundratiothe kaons N(p ,Ω ) as
lab lab
strengthofthesecutsisvariedbetween5σ and2σ. After
theapplicationoftheselectioncriteriathefinalsignal-to- d2σ Mtarget
= N(p ,Ω )· ·
backgroundratiovariesbetween0.7and120. Theimpact dp dΩ lab lab ρ ·d ·N
lab lab target target A
of the cuts on the mass distributions is as well shown in
1 1 1
Fig.3(labelled“withTOFTriggerandCuts”). Inmany · · · (2)
N f (p ,Ω ) ǫ(p )
casestheremainingbackgroundisrathersmallascanbe proj acc lab lab lab
clearlyseeninthetwolowermassdistributionsmeasured withM beingthemolarmass,ρ beingtheden-
target target
at1.93AGeV.Eveninthe caseoflow beamenergyand sityandd beingthethicknessofthetargetmaterial.
target
low particle momenta a clear K+ signal can be observed N denotes Avogadro’s constant and N the number
A proj
after applying the selection criteria (upper panel, please of projectiles impinging on the target.
note the logarithmic scale). The correction for the geometrical acceptance of the
In order to subtract the remaining background in the spectrometerandfortheparticledecayf (p ,Ω )is
acc lab lab
mass distributions, a combined fit using a Gaussian and calculated using a GEANT simulation. The simulated
a polynomial function to the mass distribution is per- data sets are analyzed with the same analysis procedure
formed within a window around the kaon mass. The astheexperimentaldata. Thecorrectionisdeducedfrom
polynomial part is used to estimate the background be- the ratio of particles found after the analysis to those
low the kaon peak and is subtracted. Figure 4 shows initially simulated.
6
r ]
rigge 1 -1V c)
t Ge -3
e (10
n/
r
a
0.5 b
[
)
Wd
p
0 /(d10 -4 Bdipole=0.6 T Bdipole=0.9 T Bdipole=1.4 T
cut 2sd 0 0.2 0.4 0.6 0.8 1 1.2 1.4
1 p [GeV/c]
e lab
FIG.6: (Color online)Differentialcross section asafunction
0.5 of p for K+ in Ni+Ni collisions at 1.1 A GeV at θ =
lab lab
40◦. Thedifferentsymbolsdenotedatameasuredatdifferent
magnetic field settings.
B =0.6 T B =0.9 T B =1.4 T
dipole dipole dipole
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
results to efficiencies calculated from real data in cases
p [GeV/c]
lab where this is possible. The resulting efficiencies range
from75%to100%. FortheexampleNi+Niat1.1AGeV
FIG. 5: (Color online) Trigger efficiencies ǫtrigger(plab) for they are depicted in the lower panel of Fig. 5.
Ni+Niat1.1AGeVforthethreemagneticfieldsettingsmea- Figure 6 shows the resulting differential cross sections
sured (upper panel), and efficiencies of the applied selection for K+ mesons in Ni+Ni collisions at 1.1 A GeV at
criteria ǫcut(plab) (lower panel) for the same data set. θlab = 40◦ according to Eq. (2) as a function of plab.
This momentum distribution consists of data measured
at three different magnetic field settings (|B |=0.6,
dipole
Thetotalefficiencyǫ(p )iscalculatedbymultiplying 0.9,and1.4T)whichareanalyzedseparatelybutoverlap
lab
the detector, the DAQ, and the tracking efficiencies de- very well.
scribedbeforeaswellasthetriggerefficiencyǫ (p )
trigger lab
and the efficiency of the application of the selection cri-
teria ǫ (p ). III. EXPERIMENTAL RESULTS
cut lab
To determine the efficiency of the trigger system
(which is based on particle velocities) pions and pro- A. Inclusive Reactions
tons measured at magnetic fields scaled by the mass ra-
tios mpion/mkaon or mproton/mkaon are used which then In this section the inclusive cross sections for the pro-
have the same velocities as kaons measured at the nom- duction of K+ and of K− mesons in C+C, in Ni+Ni and
inal fields. These pions and protons are called “TOF- in Au+Au collisions are presented as a function of their
simulatedkaons”in the following. Using anopentrigger laboratorymomentump aswellasoftheirenergyE
lab c.m.
conditionthat forces everyeventfor which a particle en- andtheiremissionangleθ inthecenter-of-momentum
c.m.
ters the spectrometer to be recorded (“w/o TOF”) and frame. Inclusive means that no centrality selection has
keepingtrackofthedecisionstheTOFtriggerwouldhave been applied to the data, neither in the analysis nor im-
taken, the efficiency of the TOF trigger can be deter- plicitly by the experimental setup or the trigger. Let us
mined. The resulting trigger efficiencies are larger than recallthatthetriggerisgeneratedbyatime-of-flightsig-
90% but they depend on the particle momentum. The nalinthespectrometerandthatthemultiplicitydetector
upper panel of Fig. 5 shows ǫtrigger(plab) for Ni+Ni at is not part of the trigger system. The determination of
1.1AGeVforthethreemagneticfieldsettingsmeasured the functional dependencies of the production cross sec-
(|Bdipole|=0.6, 0.9, and 1.4 T). tionsonEc.m. andonθc.m. allowsforanextrapolationto
Theefficiencyoftheappliedselectioncriteriaasafunc- phasespaceareasnotcoveredbytheexperimentandfora
tionofp isdeterminedusingthebackground-freemea- determinationofintegratedproductionyields. Allresults
lab
surements as described above. In some data sets the of this section are summarized in Table II. Throughout
statistics of these settings was not sufficient. In these thefiguresofthispaperweuseaconsistentcolorcodefor
cases the efficiencies of the “geometrical cuts” were de- aneasydistinctionofthecollisionsystemswhileofcourse
terminedusingGEANTsimulations,theefficiencyofthe keepingfull descriptionsforblack-and-whiteprintedver-
“velocitycut”wasdeterminedusingthe“TOF-simulated sions: Results ofAu+Au collisions appearin red, Ni+Ni
kaons”. Thismethodhasbeenvalidatedbycomparingits in blue, and C+C in green.
7
Someofthedatasetspresentedinthissectionarepub-
]
)
lished here for the first time, some have already been -1c -1 K+
published previously [7, 19, 20, 29]. As slightly different V 10
procedures have been used in these publications to ex- e
G
trapolateandtointegratethedata,wehaverecalculated ( -2
/10
the total production cross sections using one consistent n
r
procedure for all data sets. Earlier measurements with ba -3 Au+Au, 1.5AGeV
large errors are not taken into account [36, 37, 38]. [) 10
K-
Wd -3
p 10
1. Energy Distributions d
(
/ -4
2s 10
Figure 7 shows the inclusive production cross sections d q =32o q =48o q =72o
for K+ (upper panels) and for K− (lower panels) as a -5 q lab=40o q lab=60o lab
10 lab lab
function of their momentum p in the laboratory sys-
lab 0 0.5 1
tem for three different collision systems. The upper part p [GeV/c]
of the figure depicts data taken in Au+Au collisions at lab
a beam energy of 1.5 A GeV, the middle part those for
Ni+Ni at 1.93 A GeV and the lower part those for C+C
at 1.8 A GeV. To obtain a wide coverage of the phase
] -1
sspetatcineg(sseoef Fthige.s2p)ecmtreoamsuerteemr iennttsheatlasbeovrearatolrpyoθlar ahnagvlee -1c)10 K+
lab V
been performed. The lines in Fig. 7 are the results of
e
simultaneous fits to all angular settings measured for a G10 -2
(
givensystemassumingaMaxwell-Boltzmannshapedde- n/
r
pendenceoftheinvariantproductioncrosssectiononthe ba -3 Ni+Ni, 1.93AGeV
cpeenntdeern-ocfe-monomtheentcuomsineenoefrtghyeEpco.lma.reamndissaioqnuaandgrlaetiicntdhee- [) 10 -3 K-
c.m. system θ . This procedure will be discussed in Wd10
c.m. p
detail later. d
The necessity for using a non-isotropic distribution in /( -4
10
θ is depicted in Fig. 8. Here the invariant cross sec- 2s
c.m. d
etinoenrsgyσininv =thEe cdd.3pmσ3.asryessthemownEas a−fumnctci2onfoorfAthue+kAinuetaict 10 -5 qq llaabb==3420oo qq llaabb==5600oo
c.m. 0 0 0.5 1
1.5 A GeV. Full symbols denote K+, open symbols K−. p [GeV/c]
The data measured at a small angle in the laboratory lab
system(K+: θlab =32◦,K−: θlab =40◦)aredepictedby ])
circles, those measured at a large angle (K+: θlab =72◦, -1c10 -3 K+
K−: θlab = 60◦) are represented by squares. The lines V
are Maxwell-Boltzmann distributions Ge
-4
d3σ Ec.m. n/(10
Edp3 ∼ Ec.m.exp(cid:18)− T (cid:19) (3) bar -5 C+C, 1.8AGeV
[ 10
fitted to the data with T being the inverse slope param- )
eter. For an isotropic emission in the c.m. system all Wd -5 K-
spectra of a given particle type are expected to fall on p 10
d
top of each other regardless of the laboratory angle at (
/ -6
which they have been measured. For K+ mesons this 2s 10
d
is clearly not the case pointing towards an anisotropic q =32o q =48o
emission. 10 -7 q llaabb=40o q llaabb=60o
Since the distributions have been measured at fixed 0 0.5 1
values of θ in the laboratory, data points at different p [GeV/c]
lab
lab
particle energies correspond to different emission angles
θ inthec.m.system. Therefore,thisanisotropymight
c.m. FIG.7: (Color online) Inclusiveproduction cross sections for
affect the determination of the inverse slope parameter K+andforK−asafunctionofthelaboratorymomentump
lab
T of the energy spectra if data measured at a fixed θlab for inclusivereactions of Au+Auat 1.5 A GeV (upperpart),
would be transformed into the c.m. system and then fit- of Ni+Niat 1.93 A GeV (middle) and of C+C at 1.8 A GeV
ted. (lower part). The lines represent a simultaneous fit to all
laboratory anglesusingthedistributionaccordingtoEq.(5).
8
] ]
-3c) Au+Au , Ebeam=1.5AGeV -3c) 1 Au+Au K+ 11..50 AGeV
2V 1 2V 10 -1 00..86
e K+, q =32o e -2
G lab G 10
n/(10 -1 K+, q lab=72o n/( 10 -3
ar bar 10 -4
b [ -5
3[ 10 -2 3p 10
/dp K-, q lab=40o 3s/d 10 -1 Ni+Ni 111...9513 AGeV
3sE d10 -3 K-, q lab=60o E d 10 -2
-3
-4 10
10
0 0.2 0.4 -4
E -m c2 [GeV] 10
c.m. 0 10 -2 C+C 2.0 AGeV
1.8
-3 1.5
FIG. 8: (Color online) Invariant cross sections for K+ (full 10 1.2
− -4 1.0
symbols)andforK (opensymbols)ininclusiveAu+Aucol- 10 0.8
lisionsat1.5AGeV,bothatdifferentlaboratoryangles. The -5
10
linesrepresentfitsaccordingtoEq.(3). Theobservationthat -6
thedatameasuredatdifferentlaboratory angles donotcoin- 10
-7
cide indicates a non-isotropic polar-angle distribution. 10
0 0.2 0.4
E -m c2 [GeV]
c.m. 0
Therefore, we created “midrapidity distributions” by
selecting data points within θc.m. =90◦±10◦ from mea- 3]) Au+Au K- 1.5 AGeV
surements at various laboratory angles. The results are -c -2
shown in Fig. 9, in the upper part for K+, in the lower 2 10
V
partfor K−. The figure summarizes the energy distribu- e
G
tionsoftheK+ andoftheK− productionasmeasuredin /( 10 -3
n
three different collision systems (Au+Au, Ni+Ni, C+C) r
a
atdifferentincidentenergies(0.6AGeVupto2AGeV). b -4
ThemeasurementsofK+ inAu+Auat1.135AGeVand 3[ 10
p
of K− in C+C at 1.5 A GeV are not displayed in Fig. 9 d -2 Ni+Ni 1.93 AGeV
since they do not cover midrapidity. The lines are fits / 10 1.5
3s
to the data according to Eq. (3). The resulting inverse E d 10 -3
slope parameters T are given in Table II.
midrap
-4
10
2. Polar Angle Distributions -5
10
-4 C+C 2.0 AGeV
To extract the angular emission pattern we assume 10 1.8
that the dependence of the invariant cross sections on
the polarangleθ andonthe energyE canbe fac- -5
c.m. c.m. 10
torized. The energy dependence is determined at midra-
pidity byfitting Maxwell-Boltzmanndistributionsto the
-6
data as describedaboveandshowninFig. 9. As already 10
mentioned, each of the data points measured at a given
0 0.2 0.4
center-of-momentum energy Ec.m. and a laboratory an- E -m c2 [GeV]
gle θ correspondsto a different emissionangle θ in c.m. 0
lab c.m.
the center-of-momentum frame.
FIG. 9: (Color online) Inclusive invariant cross sections at
To disentangle the dependencies on the energy and on midrapidity as a function of the kinetic energy Ec.m.−m0c2
the polar emission angle we normalized each measured for K+ (upper part) and for K− (lower part) for the various
data point σinv(Ec.m.,θc.m.) to the corresponding value collision systems and beam energies measured. The midra-
σinv(Ec.m.,θc.m. = 90◦). The latter is determined us- pidity condition is a selection of θc.m. =90◦±10◦.
ing the fits to “midrapidity distributions” according to
9
ditionally performed simultaneous fits to all momentum
o0) distributionsmeasuredatdifferentlaboratoryanglesθlab
(9 Au+Au K+ Au+Au K- for a given system using the combined function
nv 2
i
qs()/invc.m. 1 Edd3pσ3 = C(cid:2)1+as2fcos2(θc.m.)(cid:3)Ec.m.exp(cid:18)−ETcs.mf .(cid:19)(5)
s a2=1.3±0.1 a2=0.7±0.3 with as2f, Tsf and the normalization C being the three
0 variable parameters. The results of this procedure are
-0.5 0 0.5 -0.5 0 0.5
denoted by the super(sub)script ’sf’. For Au+Au at
cos(q )
c.m. 1.5AGeV,Ni+Niat1.93AGeV,andC+Cat1.8AGeV
the results of these fits are shownas solid lines in Fig. 7.
)
o0 The parameters obtained for all collision systems at all
(9nv 2 Ni+Ni K+ Ni+Ni K- beam energies are given in Table II. They agree very
i well with the values obtained by the two-step procedure
s)/c.m. denotedbyTmidrap andbyad2iv. Thecombinedfitsinad-
q( 1 ditionprovidethe correlationsbetweenthe three param-
v
in etersandthusthefullerrormatrixwhichisnecessaryfor
s a=0.9±0.1 a=0.7±0.1 calculating the errors of the integrated production cross
2 2
0 sections. In those cases for which only one angle has
-0.5 0 0.5 -0.5 0 0.5
cos(q ) been measured we take an interval for the polar angle
c.m. anisotropy asf, denoted by square brackets in Table II,
2
with values set according to the trend at neighboring
FIG.10: (Coloronline)Polarangledistributionsforinclusive
beam energies. This variationof asf yields additional er-
Au+Au collisions at 1.5 A GeV (upper part) and Ni+Ni at 2
rorsonthe inverseslope parametersT aswellasonthe
1.93AGeV(lowerpart). Fullsymbolsdenotemeasureddata, sf
opensymbolsarereflectedatθc.m. =90◦. Thelinesrepresent integratedcrosssectionsastaggedbythesuperscript’a2’
fitsaccording to Eq. (4). in Table II.
Eq. (3). Assuming that the energy dependence of the 3. Total Production Cross Sections
kaon production is fully described by these midrapidity
fitstheresultsarethepolar-angleemissionpattern. They
The results of the simultaneous fits have been used to
areshowninFig.10asafunctionofcos(θ ),intheup-
c.m. extrapolate the data to phase-space regions not covered
per part for Au+Au at 1.5 A GeV and in the lower part
bytheexperimentandtocalculatetotalproductioncross
forNi+Niat1.93AGeV.Fullsymbolsaremeasureddata
sections by integrating Eq. (5) over the full phase space.
points, open symbols have been reflected at θ = 90◦
c.m. The extrapolation in E contributes with about 35%
c.m.
since for mass-symmetric systems the polar angle distri-
to the total production cross sections. The resulting to-
butions have to be symmetric around θc.m. = 90◦. Both tal production cross sections for K+ and for K− for all
systemsshowaforward-backwardpreferenceintheemis-
collision systems and for all beam energies are summa-
sionpatternwhichismorepronouncedforK+ (lefthand
rized in Table II. The error bars of the data points in
side) than for K− (right hand side).
the figures showing energy spectra and polar angle dis-
Toquantifytheanisotropy,thedistributionshavebeen
tributions contain the statistical uncertainties as well as
fitted with a quadratic dependence on cos(θ )
c.m. point to point systematic errors due to the background
subtraction. The overall systematic error of the abso-
dσ
dcos(θ ) ∼ 1 + ad2ivcos2(θc.m.) (4) lute normalizationis stated separately in Table II and is
c.m. quadraticallyadded to the statistical errorsin allfigures
asdepictedbythelinesinthefigure. Thisprocedurehas comparing cross section or multiplicities from different
beenappliedtomostdatasets resultinginthe valuesfor collision systems.
adiv as given in Table II. In the cases for which only In several cases only one polar angle has been mea-
2
one laboratory angle has been measured the coverage in sured. As already described for the inverse slope param-
θ is rather small making the determination of adiv etersT inthe previoussection,foreachofthosecasesan
c.m. 2
impossible. intervalfor a2 guided by the systematics givenby neigh-
The super(sub)scripts ’div’ for the angular anisotropy boring beam energies has been used to determine an ad-
and’midrap’fortheinverseslopeparametersareusedfor ditional error on the integrated cross section σ denoted
thetwo-stepprocedurepresentedabove. Sincetheenergy by the superscript ’a2’ in Table II.
dependenceofthekaonproductioniswelldescribedbya Part of the data has been published earlier with the
Maxwell-Boltzmanndistributionandthepolarangledis- methods to extrapolate the measured data to the full
tributionbyaquadraticdependenceoncos(θ )wead- phase space being slightly different in the various publi-
c.m.
10
cations. In this paper, we consistently apply one single
method to extrapolate and integrate the data. A
/
For C+C collisions σ and T for K+ and for K− were M K+ K-
published[19]assumingtheangularanisotropyforallin- -4 Au+Au
10 Ni+Ni
cident energies to contribute with 20% to the total cross C+C
sectionindependentoftheincidentenergywhichisequiv-
alent to a2 = 0.6. Now we determine a2 for each mea- -5
10
surement separately. The differences between the values
for σ and T in Table II and those published in [19] are
nevertheless smaller then the statistical errors. -6
Inthe caseofNi+Ni,crosssectionsforthe K+ andfor 10
the K− production at 1.93 A GeV have been published
in [20] with the angular anisotropy being taken from a
0 0.5 1 1.5 2
two-step procedure rather than from a simultaneous fit. E [AGeV]
Also in this case the differences between the results in beam
Table II and the previously published values are smaller
FIG. 11: (Color online) Multiplicities of K+ (full symbols)
than the statistical errors.
andofK− mesons(opensymbols)permassnumberAofthe
For Au+Au σ, T and a have been published for
2 respective collision system as a function of the beam energy.
K+ [7]. The results in Table II for 0.6, 0.8, 1.0 and
The lines represent fitsto thedata according to Eq.(6).
1.135 A GeV differ less than the statistical errors from
the published values. For K+ at 1.5 A GeV the results
published in [7] are: σ =267±30 mb, T =100±5 MeV
and a =1.06±0.3. They correspondto a low statistics
2
measurementusingathickertargetreducingtheeffective
beamenergyforthe K+ productionto1.46AGeV.This B. Centrality Dependence
difference in effective energy accounts for a difference of
about 10% in cross section compared to the new high
statistics experiment reported upon in this paper using
The collision centrality was derived from the multi-
a thinner target (with E = 1.48 A GeV). In addition
eff
plicity of charged particles measured in the Large-Angle
in the experiment described in [7] the anisotropy in the
Hodoscope (Mult ). Figure 12 shows the respective
polar angle emission pattern was underestimated due to LAH
multiplicity distributions for Au+Au at 1.5 A GeV (up-
a reduced coverage in θ accounting for an additional
lab
per panel) and for Ni+Ni at 1.93 A GeV (lower panel)
5% difference in the cross section.
measured with a multiplicity trigger. In order to study
To calculate particle multiplicities M the integrated
the centrality dependence of the K+ and of the K− pro-
production cross sections σ (see Table II) need to be di-
duction the data were grouped into five centrality bins
vided by the total reaction cross section σ which can-
r
both for Ni+Ni at 1.5 and at 1.93 A GeV as well as
not be determined easily as the particle-multiplicity dis-
for Au+Au at 1.5 A GeV. These bins are also depicted
tribution measured with a multiplicity trigger condition
in Fig. 12. The distributions have been normalized to
has a cutoff at low multiplicities (see also Sect. IIIB).
the beam intensity, to the target thickness and to the
Therefore, we determine the reaction cross sections us-
efficiency of the DAQ system so that the area between
ing Glauber calculations[39] resulting in σ (Au+Au)=
r
the respective bin boundaries represents the correspond-
6.8 barn, σ (Ni + Ni) = 3.1 barn, and σ (C + C) =
r r
ing fraction of the total reaction cross sections σ for
0.95barn. Figure11summarizesthemultiplicitiesofK+ r
a given bin. Very peripheral collisions in the first cen-
and of K− mesons as a function of the beam energy as
trality bin might be missed by the multiplicity trigger,
determinedininclusivereactions(Au+Au,Ni+Ni,C+C)
however,kaonsfromsuchperipheraleventsaremeasured
and normalized to the mass number A of the respective
since they are triggered by the time-of-flight trigger in
colliding nuclei. Both particle species exhibit strongly
the spectrometer. The fraction of σ for this most pe-
rising excitation functions as expected due to the prox- r
ripheral bin is determined by taking the inclusive total
imityofthethresholdsinbinaryNNcollisions(1.58GeV
reaction cross section from a Glauber calculation [39]
for K+, 2.5 GeV for K−). The solid lines reflect fits ac-
andsubtracting the sumofthe experimentallymeasured
cording to the formula [40]
values of the four other centrality bins. For Au+Au,
M E the five bins correspond to 0 − 5.4%, 5.4% − 18.1%,
K thr
= C T exp − , (6)
max 18.1% − 31.1%, 31.1% − 52.3%, and 52.3% − 100%
A T
(cid:20) max(cid:21) of σ from central to peripheral collisions, for Ni+Ni to
p r
with T = T ·(E )η. The variable parameters in 0−4.4%,4.4%−15.0%,15.0%−26.5%,26.5%−45.9%,
max 0 beam
the fit are C, T and η. As well for K+ as for K− the and 45.9% − 100.0% of σ . The corresponding mean
0 r
multiplicities per mass number A increase with system numbersofparticipatingnucleonsA haveaswellbeen
part
size from C+C to Au+Au at the same incident energy. calculated using Glauber calculations.