Page 1
arXiv:1004.1889v1 [hepex] 12 Apr 2010
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERNPHEP/2009029
November 22, 2009
Inclusive production of charged kaons in p+p collisions
at 158 GeV/c beam momentum and a new evaluation
of the energy dependence of kaon production
up to collider energies
T. Anticic12, B. Baatar5, J. Bartke4, L. Betev6, H. Białkowska11, B. Boimska11, J. Bracinik1,a,
V. Cerny1, O. Chvala8,b, J. Dolejsi8, V. Eckardt7, H.G. Fischer6, Z. Fodor3, E. Gładysz4,
K. Kadija12, A. Karev6, V. Kolesnikov5, M. Kowalski4, M. Kreps1,c, M. Makariev10,
A. Malakhov5, M. Mateev9, G. Melkumov5, A. Rybicki4, N. Schmitz7, P. Seyboth7, T. Susa12,
P. Szymanski11, V. Trubnikov11, D. Varga2, G. Vesztergombi3, S. Wenig6,1)
(The NA49 Collaboration)
1Comenius University, Bratislava, Slovakia
2E¨ otv¨ os Lor´ and University, Budapest, Hungary
3KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary
4H. Niewodnicza´ nski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow,
Poland
5Joint Institute for Nuclear Research, Dubna, Russia
6CERN, Geneva, Switzerland
7MaxPlanckInstitut f¨ ur Physik, Munich, Germany
8Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear
Physics, Prague, Czech Republic
9Atomic Physics Department, Sofia University St. Kliment Ohridski, Sofia, Bulgaria
10Institute for Nuclear Research and Nuclear Energy, BAS, Sofia, Bulgaria
11Institute for Nuclear Studies, Warsaw, Poland
12Rudjer Boskovic Institute, Zagreb, Croatia
anow at School of Physics and Astronomy, University of Birmingham, Birmingham, UK
bnow at UC Riverside, Riverside, CA, USA
cnow at Institut fur Experimentelle Kernphysik, Karlsruhe, DE
to be published in EPJC
1)Corresponding author: Siegfried.Wenig@cern.ch
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Abstract
New data on the production of charged kaons in p+p interactions are presented. The data
come from a sample of 4.8 million inelastic events obtained with the NA49 detector at
the CERN SPS at 158 GeV/c beam momentum. The kaons are identified by energy loss
in a large TPC tracking system. Inclusive invariant cross sections are obtained in inter
vals from 0 to 1.7 GeV/cin transverse momentum and from 0to 0.5 in Feynman x. Using
these data as a reference, a new evaluation of the energy dependence of kaon production,
including neutral kaons, is conducted over a range from 3 GeV to p+p collider energies.
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1 Introduction
Following the detailed investigation of inclusive pion [1] and baryon [2] production in
p+p interactions,thepresent paperconcentrates on thestudyofcharged kaons. It thuscompletes
a series of publications aimed at the exploration of final state hadrons in p+p collisions by using
a new set of high precision data from the NA49 detector at the CERN SPS [3]. The data have
been obtained at a beam momentum of 158 GeV/c corresponding to a centerofmass system
(cms) energy of 17.2 GeV. This matches the highest momentum per nucleon obtainable with
lead beams at the SPS, permitting the direct comparison of elementary and nuclear reactions.
In addition, the chosen cms energy marks, concerning kaon production, the transition from
thresholddominated effects with strong sdependences to the more gentle approach to higher
energies where scaling concepts become worth investigating. On the other hand the character
istic differences between K+and K−production which are directly related to the underlying
production mechanisms, as for instance associate kaon+hyperon versus K+K pair production,
are still well developed at SPS energy. They are manifest in the strong evolution of the K+/K−
ratio as a function of the kinematic variables. One of the aims of this paper is in addition the
attempt to put the availableresults from other experimentsinto perspectivewith the present data
in order to come to a quantitative evaluation of the experimental situation.
A critical assessment of the complete sdependence of kaon production seems the more
indicated as its evolution in heavy ion interactions, especially in relation to pions, is promul
gated since about two decades as a signature of ”new” physics by the creation of a deconfined
state of matter in these interactions. As all claims of this nature have to rely completely on
a comparison with elementary collisions, the detailed study of the behaviour of kaon produc
tion in p+p reactions from threshold up to RHIC and collider energies should be regarded as
a necessity in particular as the last global evaluation of this type dates back by more than 30
years [4]. A complete coverage of phase space, as far as a comparison of different experiments
is concerned, is made possible in this paper, as compared to pions [1] and baryons [2], by the
fact that there is no concern about feeddown corrections from weak hyperon decays, with the
exception of Ω decay which is negligible for all practical purposes.
This paper is arranged in the same fashion as the preceding publications [1,2]. A sum
mary of the phase space coverage of the available data from other experiments in Sect. 2 is
followed by a short presentation of the NA49 experiment, its acceptance coverage and the cor
responding binning scheme in Sect. 3. Section 4 gives details on the particle identification via
energy loss measurement as they are specific to the problem of kaon yield extraction. The eval
uation of the inclusive cross sections and of the necessary corrections is described in Sect. 5,
followed by the data presentation including a detailed data interpolation scheme in Sect. 6.
K+/K−, K/π and K/baryon ratios are presented in Sect. 7. A first step of data comparison with
data in the SPS/Fermilab energy range is taken in Sect. 8. Section 9 deals with the data inte
grated over transverse momentum and the total measured kaon yields. The data comparison is
extended, in a second step, over the range from√s ∼ 3 to ISR, RHIC and p+p collider energies
in Sect. 10. Section 11 concentrates on an evaluation of K0
and on a discussion of total kaon multiplicities as a function of√s. A comment on the influ
ence of resonance decay on the observed patterns of pTand s dependence is given in Sect. 12.
In Sect. 13 a global overview of charged and neutral kaon yields as they result from the study
of sdependence in this paper is presented, both for the pTintegrated invariant yields at xF= 0
and for the total kaon multiplicities. A summary of results and conclusion is given in Sect. 14.
Syields in relation to charged kaons
1
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2The experimental situation
Thispaper considersthedoubledifferentialinclusivecross sectionsofidentified charged
kaons,
d2σ
dxFdp2
T
,
(1)
as a function of the phase space variables defined as transverse momentum pT and reduced
longitudinal momentum
xF=
pL
√s/2
(2)
where pLdenotes the longitudinal momentum component in the cms.
If the phase space coverage of the existing data has been shown to be incomplete and
partially incompatible for pion and baryon production in the preceding publications [1,2], the
situation is even more unsatisfactory for charged kaons. A wide range of data covering essen
tially the complete energy range from kaon threshold via the PS and AGS up to the ISR and
RHIC energy has been considered here. One advantage concerning the data comparison for
kaons is the absence of feeddown from weak decays with the exception of Ω−decay which can
be safely neglected at least up to ISR energies. An overview of the available data sets is given
in Fig. 1 for K+and Fig. 2 for K−in the xF/pTplane.
00.20.4
x
0.60.8
[12]
[13]
[14]
d)
+
K
c)
+
K
[11]
b)
[7,8]
[9]
[10]
+
K
0
2
0.5
1
1.5
2
[5]
[6]
a)
+
K
00.20.4
x
0.60.8
g)
+
KNA49
00.20.4
x
0.60.8
f)
+
K
[2325]
[26,27]
[2830]
00.20.4
x
0.60.8
0
0.5
1
1.5
e)
+
K
[1619]
[20]
[21]
[22]
[GeV/c]
p
T
[GeV/c]
p
T
FFF
F
Figure 1: Phase space coverage of the existing K+data: a) Cosmotron/PPA [5,6], b) PS/AGS
[7–10], c)Serpukhov[11], d)SPS/Fermilab [12–14], e)ISR [16–22],f)RHIC [23–30], g)NA49
Thesubpanelsa)throughg)showsuccessivelytheenergyrangesoftheCosmotron/PPA
[5,6], PS/AGS [7–10], Serpukhov [11], SPS/Fermilab [12–14], ISR [15–22] and RHIC [23–30]
accelerators in comparison to the new data from NA49. The scarcity of data in the important
intermediate energy range around√s ∼ 10 GeV and the general lack of coverage in the low
pTand lowxFregions are clearly visible. The coverage of the NA49 data, Figs. 1g and 2g, is
2
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00.20.4
x
0.60.8
[12]
[13]
[14]
d)

K
c)

K
[11]
b)
[7,8]
[9]
[10]

K
0
2
0.5
1
1.5
2
a)

K
00.20.4
x
0.60.8
g)

KNA49
00.20.4
x
0.60.8
f)

K
[2325]
[26,27]
[2830]
00.20.4
x
0.60.8
0
0.5
1
1.5
e)

K
[1517]
[20]
[21]
[22]
[GeV/c]
p
T
[GeV/c]
p
T
FFF
F
Figure 2: Phase space coverage of the existing K−data: a) Cosmotron/PPA, b) PS/AGS [7–10],
c) Serpukhov [11], d) SPS/Fermilab [12–14], e) ISR [15–17,20–22], f) RHIC [23–30], g) NA49
essentially only limited by counting statistics towards high pT and by limitations concerning
particle identification towards high xF, in particular for K+, see Sect. 4 below.
The task of establishing data consistency over the wide range of energies considered
here is a particularly ardent one for kaons, as will be shown in the data comparison, see Sects. 8
and 10 below. This concerns especially any attempt at establishing total integrated yields where
the existing efforts evidently suffer from a gross underestimation of systematic errors. Their
relation to the total yields of K0
to SPS/Fermilab energies as well as their eventual comparison with strangeness production in
nuclear collisions should therefore be critically reconsidered.
Swhich are established with considerably higher reliability up
3The NA49 experiment, acceptance coverage and binning
The basic features of the NA49 detectors have been described in detail in [1–3]. The top
view shown in Fig. 3 recalls the main components.
The beam is a secondary hadron beam produced by 450 GeV/c primary protons imping
ing on a 10 cm long Be target. It is defined by a CEDAR Cerenkov counter, several scintillation
counters (S1, S2, V0) and a set of high precision proportional chambers (BPD13). The hydro
gen target is placed in front of two superconducting Magnets (VTX1 and VTX2). Four large
volumeTimeProjectionChambers (VTPC1 and VTPC2 insidethemagneticfields, MTPCLand
MTPCR downstream of the magnets) provide for charged particle tracking and identification.
A smaller Time Projection Chamber (GTPC) placed between the two magnets together with
two Multiwire Proportional Chambers (VPC1 and VPC2) in forward direction allows tracking
in the high momentum region through the gaps between the principal track detectors. A Ring
Calorimeter (RCal) closes the detector setup 18 m downstream of the target.
The phase space region accessible to kaon detection is essentially only limited by the
availablenumberof4.6 M inelasticevents.It spans arange oftransversemomentabetween 0.05
and 1.7 GeV/c for K+and K−and Feynman xFbetween 0 and 0.5 for K−. For K+a limitation
3
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Target
VTPC 1VTPC 2
MTPC R
MTPC L
GTPC
13.05 m
x
1 m
z
1.8 m
S4
VPC1
VPC2
RCal
55 m
34 m
10 m
4 m
Target
BPD1 BPD2BPD3
VTX 1VTX 2
S1
S2V0 S4
CEDAR
erenkovC
Beam and trigger definition elements
Figure 3: NA49 detector layout and real tracks of a typical mean multiplicity p+p event. The
open circles are the points registered in the TPC’s, the dotted lines are the interpolated trajec
tories between the track segments and the extrapolations to the event vertex in the LH2target.
The beam and trigger definition counters are presented in the inset
to xF≤ 0.4 is imposed by the constraints on particle identification discussed in Sect. 4 below.
These kinematical regions are subdivided into bins in the xF/pTplane which vary ac
cording to the measured particle yields, effects of finite bin widths being corrected for in the
evaluation of the inclusive cross sections (Sect. 5). The resulting binning schemes are shown in
Fig. 4 also indicating different ranges of the corresponding statistical errors.
[GeV/c]
p
T
F
x
00.10.20.30.40.50.6
< 3 %
310 %
> 10 %
b)

K
F
x
00.10.20.30.40.50.6
0
0.5
1
1.5
2
< 3 %
310 %
> 10 %
a)
+
K
Figure 4: Binning schemes in xFand pTfor a) K+and b) K−together with information on the
statistical errors
4
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4 Particle identification
The identification of kaons by their ionization energy loss in the gas of the TPC detector
system meets with specific problems if compared to pion [1] and baryon [2] selection. This
specificity has several reasons:
– Corresponding to the momentum range of the NA49 data the ionization energy loss has
to be determined in the region of the relativisticrise of the energy deposit, with the kaon
energy loss positioned in between the one for baryons and for pions.
– The relative distance in dE/dx between the different particle species is small and varies
from only 4.5 to 7% for kaons with respect to protons and from 6.5 to 14% with respect
to pions, over the xF range of the present data, with an rms width of the energy loss
distributions of typically 3%. This creates an appreciable overlap problem over most of
the phase space investigated.
– High precision in the determination of the absolute position of the mean truncated en
ergy loss per particle species and of the corresponding widths is therefore mandatory.
– The relative production yield of kaons is generally small as compared to pions, with
K/π ratios on the level of 5–30% for K+and 5–20% for K−. In addition, for K+the fast
decrease of the K+/p ratio from typically 1 at xF= 0 to less than 5% at xF= 0.4 finally
imposes a limit on the applicability of dE/dx identification towards high xFvalues.
This general situation may be visualized by looking at a couple of typical dE/dx distri
butions for different xFregions as shown in Fig. 5.
Entries
Entries
dE/dx [MIP]dE/dx [MIP]
π

Kp
= 0.4 GeV/c
= 0.05
F
x
T
p
b)
0
5000
10000
15000
20000
+
π
+
Kp
= 0.4 GeV/c
= 0.05
F
x
T
p
a)
11.52
π

Kp
= 0.4 GeV/c
= 0.25
F
x
T
p
d)
11.52
0
1000
2000
3000
4000
+
π
+
K
p
= 0.4 GeV/c
= 0.25
F
x
T
p
c)
Figure 5: dE/dx distributions for K+and K−bins at xF= 0.05, pT= 0.4 GeV/c and xF= 0.25,
pT= 0.4 GeV/c superimposed with results of the fitted distributions
As already described in [2] a considerable effort has been invested into the improved
control of the analog response of the detector. Several aspects and results of this work, in partic
ular as far as kaon identification is concerned, will be discussed in the following subsections.
5
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4.1 NonGaussian shape of the dE/dx distributions
Due to the small K/π and K/p ratios mentioned above, the precise description of the
tails of the energy loss distributions of the dominant particle species becomes important. The
extraction of kaon yields becomes indeed sensitive to small deviations in the upper tail of the
proton and in the lower tail of the pion distributions for the extreme yield ratios mentioned
above,asisalso apparentfromtheexamplesshowninFig. 5. Eventualasymmetrieswithrespect
to the generally assumed Gaussian shape of the energy loss distributions have therefore to be
carefully investigated as they will influence both the fitted central position and the extracted
yields of the kaons. A detailed study of the shape of the dE/dx distributions has therefore been
performed both experimentally and by analytical calculation.
By selecting long tracks in the NA49 TPC system which pass both through the VTPC
and the MTPC detectors one may use the energy deposit in one of the TPC’s to sharply select
a specific particle type of high yield, for instance pions or protons. The dE/dx deposit in the
other TPC will then allow a precise shape determination. An example is shown in Fig. 6 for the
selection of pions at xF= 0.02 and pT= 0.3 GeV/c in the VTPC. The corresponding distribution
of the truncated mean for 90 samples in the MTPC is presented in Fig. 6a together with a
Gaussian fit.
dE/dx [MIP]
1.21.3 1.41.5
Data/Gaussian
0
0.5
1
1.5
2
b)
= 0.02
F
x
= 0.2 GeV/c
= 0.3 GeV/c
T
p
p
T
dE/dx [MIP]
1.21.31.4 1.5
Entries
10
2
10
3
10
4
10
a)
= 0.02
F
x
= 0.3 GeV/c
T
p
data
pion fit
Figure 6: a) Conventional Gaussian fit of the MTPC dE/dx distribution, for tracks with pion
selection using the VTPC dE/dx; b) Ratio of data and fit function
The small but very evident skewness of the truncated energy loss distribution is ex
pressed in Fig. 6b by the ratio of the experimental data to a Gaussian fit. This ratio may be
described by a cubic polynomial form with one normalization parameter Z, shown as the full
line in Fig. 6b.
(Data)/(Gaussian) ≈ 1 + Z(g3− 3g),
(3)
where g is the distance from the mean of the dE/dx distribution, normalized to the rms of the
Gaussian fit,
g =1
σ
??dE
dx
?
−
?dE
dx
??
.
(4)
6
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The parameter Z is related to the number of measured points, Np, on each track, and the
central dE/dx value by the relation
Z = z0N−β
p
?dE
dx
?γ
,
(5)
with β and γ experimentally determined to 0.5 [1] and 0.4±0.2, respectively. Together with the
relation:
σ
(dE/dx)= σ0N−β
p
?dE
dx
?α
,
(6)
assuming α = γ which is a safe assumption regarding the sizeable error in the determination of
γ, z0is obtained as
z0= 0.215 ± 0.02
z0= 0.21 ± 0.02
for the VTPC
for the MTPC.
(7)
A Monte Carlo simulation based on the Photon Absorption Ionization (PAI) model [31]
confirmed these results, demonstrating that the shape distortion is indeed a remnant of the basi
cally asymmetric Landau distribution of ionization energy loss.
4.2 Position and width of the energy loss distributions
Particle identificationproceeds, in each defined bin ofphase space, via aχ2optimization
procedure between the measured energy loss distributions and four single particle dE/dx dis
tributions of known shape but a priori unknown positions and widths for electrons, pions, kaons
and protons, respectively. Due to the generally small fraction of electrons and their position in
the density plateau of the energy loss function, and due to the known dependence of the dE/dx
resolution on the dE/dx value for each particle species [1], (Eq. 6), the problem reduces in
practice to the determination of eight quantities: three absolute positions of the energy loss of
π, K, p, one width parameter and four yield values which correspond to the particle cross sec
tions to be determined. If the fit of the predominant particle species like pions and protons in
general presents no problems, the situation is more critical for the kaons. Here it is in principle
the central kaon position and the overall rms width of the dE/dx distributions which are liable
to create systematic yield variations. In the ideal case, the detector response should reproduce
exact scaling in the p/m variable as implied by the BetheBloch function of ionization energy
loss (BB), with p the lab momentum and m the particle mass. As shown in [1–3] this scaling is
fulfilled for pions and protons in the NA49 detector on the subpercent level. The precision of
the dE/dx fitting procedure allows for a quantification of the remnant deviations δ with respect
to the BetheBloch parametrization as a function of xFand pT
δ(xF,pT) =dE
dx(xF,pT) − BB
(8)
in units of minimumionization (MIP), where dE/dx is the mean truncated energy loss [1]. This
is presented in Fig. 7 for the mean deviation of π+and protons.
The observed deviations are due to residual errors in the calibration of the detector re
sponse and in the transformation between the BetheBloch parametrizations of the different
gases used in the VTPC and MTPC detectors [3]. They stay in general below the level of
±0.005. The fitted shifts of the kaon position, as characterized by their difference to the pion
7
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[GeV/c]
T
p
0 0.51 1.5
〉
,p
+
π
δ 〈
0.005
0
0.005
F
x
0.0
0.025
0.05
0.1
0.3
0.15
0.2
0.25
0.4
Figure 7: Mean deviation ?δπ+,p?, in units of minimumionization, of π+and proton dE/dx with
respect to the BetheBloch parametrization as a function of pTfor different values of xF
position δK− δπ, are shown in Fig. 8 as a function of xFand averaged over pT, the error bars
representing the rms deviation of the averages.
F
x
0 0.20.4
〉
π
δ 

δ 〈
K
0.005
0
0.005
0.01
b)

K
F
x
0 0.2 0.4
〉
+
π
δ 
+
K
δ 〈
0.005
0
0.005
0.01
a)
+
K
Figure 8: Mean deviations in units of minimum ionization of a) K+and b) K−with respect to
the pion position ?δK± − δπ±? as a function of xF, averaged over pT
Evidently the measured positions fall well within the margin of ±0.005 in units of min
imum ionization as obtained for pions and protons. The similarity, within errors, between the
results for K+and K−indicates systematic detector response effects as the principle source of
the measured deviations.
The fitted rms widths of the dE/dx distributions, characterized by their relative devia
tion from the calculated expectation value (Eq. 6 above), are shown in Fig. 9 as a function of
xF, after averaging over pT.
The results show that the predicted widths are reproduced with an accuracy within a
few percent of the expected values, with a slight systematic upwards trend as a function of xF
closely similar for K+and K−.
8
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F
x
0 0.2 0.4
rel
σ
0.98
1
1.02
1.04
+
K
K

Figure 9: Relative rms width σrelas a function of xFfor K+and K−, averaged over pT
4.3 Estimation of systematic errors
The dependence of the fitted kaon yields on the four parameters mentioned above,
namely the positions of pions, kaons, protons, and the relative rms width of the fits, has been
studied in detail. It appears that only two of these parameters are liable to produce noticeable
systematic effects. These are the kaon position and the rms width. By enforcing a range of fixed
values of these parameters, their influence on the extraction of kaon yields may be obtained.
This is demonstrated in Fig. 10 for the dependence on kaon position and in Fig. 11 for the de
pendence on the relative rms width, the error bars in each plot indicating the rms size of the pT
dependence.
F
x
0 0.1 0.2 0.30.4
slope of the yield variation [%/0.001]
3
2
1
0
1
+
K
K

Figure 10: Slope of the yield variation given in % per assumed kaon shift of 0.001 for K+and
K−as a function of xF, averaged over pT
Several aspects of this study are noteworthy:
– As far as the influence of the kaon position uncertainty is concerned, and taking into
account the size of the measured deviations from pions and protons and their rms fluc
tuation (see Fig. 8) the related errors stay on the level of less than 1% up to xF= 0.2.
Above this value the K+yield reacts very critically on the fitted position. This is related
to the proton yield which becomes rapidly overwhelming towards high xF.
– Concerning the rms width the situation is somewhat more critical especially for K+.
Here, allowing for a systematic error of about 0.5% in the fitted relative rms, Fig. 9,
9
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F
x
0 0.1 0.20.3 0.4
slope of the yield variation [%/0.005]
10
8
6
4
2
0
+
K

K
Figure 11: Slope of the yield variation given in % per assumed change of σrelof 0.005 for K+
and K−as a function of xF, averaged over pT
the corresponding yield error reaches values of about 2% at xF= 0.2 and about 10% at
xF= 0.4. This is again measuring the influence of the large proton fraction. For K−on
the other hand, the systematic error stays below the 2% level for the whole xFregion
investigated.
The systematic errors estimated here have been included in the error estimation in Ta
ble 1.
4.4Fit stability and xFlimit for kaon yield extraction
The fitting procedure described above results in stable values for all eight parameters
involved for xFvalues below about 0.25 for K+and below 0.3 for K−. This is to be understood
in the sense that the χ2optimization procedure converges to a welldefined minimum in all
variables with reasonable values for the ratio of χ2over the degrees of freedom. For higher xF
values the fits tend to become unstable in the sense that certain variables tend to ”run away”
into unphysical configurations. In the present case of extraction of kaon yields this concerns
basically only the kaon position in the dE/dx variable and the rms width parameter of the
energy loss distributions, as the pion and proton positions are always well constrained even in
the critical regions of phase space. The problem is of course connected to the high sensitivity of
the extracted kaon yield on these two parameters in relation to the small K/π and K/p ratios as
discussed in the preceding section.
As the evolution of both the kaon position and the rms width with the phase space
variablesxFand pTshowsno indicationof any rapid variationup to thelimitsoffitting stability,
and as indeed the geometrical configuration of the tracks in the TPC detectors shows a smooth
and slow dependence on the track momenta in the regions concerned, it has been decided to
extend the xF range up to 0.4 for K+and to 0.5 for K−by imposing constraints on the two
criticalparameters.Thisisrealizedbyconstrainingthekaonpositiontofixedvalueswithrespect
to the pions, as indicated by the extrapolated lines in Fig. 8, and by also fixing the rms widths to
the values following from the smooth extrapolation indicated in Fig. 9. The expected statistical
error margins, allowing for reasonable values for the uncertainties in the quantities concerned,
see Figs. 10 and 11, have been added in quadrature to the statistical errors.
10
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4.5 Estimation of statistical errors
It has been shownin[2]that theestimationofthestatisticalerroroftheextractedparticle
yields has to take into account the dependence of the fit result on all parameters fitted via the
covariance matrix. This means that the inverse square root of the predicted numbers of each
particle species is only a first approximation to the relative statistical error. The fluctuations
of the fitted particle positions discussed above and their contributions to the error of the yield
parameters are intercorrelated with the particle ratios and with the relative distances of the
energy deposits in the dE/dx variable. The method outlined in [2] has been applied to all
extracted kaon yields and results in the statistical errors quoted in the data tables, Sect. 6 below.
The ratio Rstatbetween the full statistical error and the inverse square root of the extracted
yields is a sensitive indicator of the fluctuations inherent in the fitting method itself. It can vary
drastically over phase space according to the correlation with the particle ratios and the relative
positions with respect to the BetheBloch function. This is visible in the distributions of the
ratio Rstatdefined above and shown in Fig. 12 for K+and K−in two different regions of xF.
Entries
stat
R
1 1.52 2.5
0
5
10
< 0.2
mean = 1.39
F
x a)
+
K
0.25
≤
F
x
≤
0.2
mean = 2.11
stat
R
1 1.52 2.5
0
5
10
15
< 0.2
mean = 1.17
F
x b)

K
0.25
≤
F
x
≤
0.2
mean = 1.49
Figure 12: Rstat= σstat/(1/√N) for the bins xF< 0.2 (solid line) and 0.2 ≤ xF≥ 0.25 (dashed
line); a) K+and b) K−
Rstatis in general bigger for K+than for K−due to the large p/p ratio. In both cases the
forward bins in xFshow a strong increase in Rstatwhich indicates the approach to the limit of
stability of the fit procedure in particular for K+. In the higher xFbins, xF= 0.3 and xF= 0.4
the constraints imposed on some fit parameters, Sect. 4.4, limit of course also the range of the
possible statistical fluctuations. Here, the problem has to be tracked by the evaluation of the
corresponding systematic errors.
5Evaluation of invariant cross sections and corrections
The experimental evaluation of the invariant cross section
f(xF,pT) = E(xF,pT) ·d3σ
dp3(xF,pT)
(9)
follows the methods described in [1]. This includes the absolutenormalization via the measured
trigger cross section of 28.23 mb and the number of events originating from the liquid hydrogen
target. The trigger is defined by a system of scintillation counters and proportional chambers on
the incoming beam plus a downstream scintillator vetoing noninteracting beam particles.
11
Page 14
5.1 Empty target correction
Due to the small empty/full target ratio of 9% and the larger fraction of zero prong
events in the empty target sample, the empty target contribution may be treated as a small
correction as argued in [1]. This correction is, within the statistical errors, equal for K+and K−
and independent on pTand xF. It is compatible with the one given for pions [1] and protons [2]
and is presented in Fig. 13 as a function of xF.
F
x
0 0.20.4
factor for ET correction
0.98
1
1.02
1.04
1.06
1.08
Figure 13: Empty target correction for K+and K−as a function of xF, averaged over pT
5.2 Trigger bias correction
This correction is necessitated by the interaction trigger which uses a small scintillator
placed between the two magnets (S4 in Fig. 3) in anticoincidence with the beam signal. This
triggervetoeseventswithfastforward particlesandtherebynecessitatesatriggerbiascorrection
whichcan in principledependbothon particletypeand onthekinematicvariables.Asdescribed
in detail in [1] the correction is quantified experimentally by increasing the diameter of the S4
veto counter offline and extrapolating the observed change in cross sections to diameter zero.
For the case of kaons, the correction turns out to be within errors independent on pTand similar
for K+and K−. Its xFdependence is shown in Fig. 14.
trig. bias corr. [%]
F
x
0 0.20.4
b)

K
→
p+p
F
x
0 0.2 0.4
0
2
4
6
8
a)
+
K
→
p+p
Figure 14: Triggerbias correction as a function of xFfor a) K+and b) K−. The lines correspond
to the parametrization of the correction
12
Page 15
5.3 Reinteraction in the target
This correction has been evaluated [1] using the PYTHIA event generator. It is pTinde
pendent within the available event statistics. The xFdependence is shown in Fig. 15.
F
x
0 0.2 0.4
target reinteraction corr. [%]
2
1
0
+
K
K

Figure 15: Target reinteraction correction as a function of xF
5.4Absorption in the detector material
The correction for kaons interacting in the detector material downstream of the target is
determined using the GEANT simulation of the NA49 detector, taking account of the K+and
K−inelastic cross sections in the mostly light nuclei (Air, Plastic foils, Ceramic rods). Due to
the nonhomogeneous material distribution the correction shows some structure both in pTand
xFas presented in Fig. 16.
F
x
0 0.20.4
det. abs. corr [%]
0
1
2
3

, K
+
K
= 0.1 GeV/c
T
= 1.1 GeV/c
T
p
p
Figure 16: Correction due to the absorption of produced kaons in the downstream detector
material as a function of xFfor two pTvalues. The lines are shown to guide the eye
5.5 Kaon weak decays
Due to their decay length of about 30 m at the lowest lab momentum studied here, the
weak decay of kaons necessitates corrections of up to 7% for for kaons produced in the lowest
13
Page 16
measured xFrange. Due to the high Q value of the decay channels and unlike the weak decay
of pions, the decay products are not reconstructed to the primary vertex. This has been verified
by detailed eyescans using identified kaons with visible decays inside the TPC system. The
decay correction is therefore determined for those kaons which decay before having passed the
necessary number of pad rows for reconstruction and identification. The resulting corrections
are presented in Fig. 17.
F
x
0 0.20.4
kaon decay correction [%]
0
2
4
6
8
= 0.1 GeV/c
T
= 0.5 GeV/c
T
= 0.9 GeV/c
T
= 1.3 GeV/c
T
p
p
p
p
Figure 17: Decay correction as a function of xFat different pTvalues. The lines are shown to
guide the eye
5.6 Binning correction
The effect of finite bin sizes on the extracted inclusivecross sections is determined using
the second derivatives of the xFor pTdistributions, as discussed in detail in [1]. The associated
corrections are within the statistical errors equal for K+and K−. Examples are shown in Fig. 18
as a function of xFat fixed pTand as a function of pTat fixed xF.
binning correction [%]
F
x
0 0.10.2 0.30.4
8
6
4
2
0
2
4
a)

, K
+
K
= 0.4 GeV/c
T
p
[GeV/c]
T
p
0 0.51 1.5
b)
= 0.1
F
x
Figure 18: Binning correction, a) as a function of xFfor pT= 0.4 GeV/c and b) as a function
of pT for xF = 0.1. The crosses represent the corrections for fixed values of δxF = 0.05 and
δpT= 0.1 GeV/c, respectively, and the open circles give the corrections for the used bin widths.
The lines are shown to guide the eye
14
Page 17
5.7 Systematic errors
The systematic errors of the extracted cross sections are defined by the uncertainties of
thenormalizationand correction procedures and by a contributionfrom particleidentificationas
described in Sect. 4. In particular the uncertainties due to the corrections may be well estimated
from their distributions over all measured bins presented in Fig. 19. The corresponding error
estimates are given in Table 1.
xF≤ 0.2
K+,K−
1.5%
0.5%
0.0%
1.0%
xF≥ 0.25
K+
1.5%
0.5%
4–12%
1.0%
K−
1.5%
0.5%
0–6%
1.0%
Normalization
Tracking efficiency
Particle identification
Trigger bias
Detector absorption
Kaon decay
Target reinteraction
Binning
Total(upper limit)
Total(quadratic sum)
?
1.0% 1.0%1.0%
0.5%
4.5%
2.2%
0.5% 0.5%
8.5–16.5%
4.6–12.2%
4.5–10.5%
2.2–6.4%
Table 1: Summary of systematic errors
The linear sum of these estimations gives an upper limit of 4.5%, the quadratic sum
an effective error of 2.2% for xF ≤ 0.2. These values are close to the estimations obtained for
pions [1] and baryons [2]. In the xFregion above0.25, however, the upper limit(quadratic sum)
can reach 16.5%(12.2%) for K+and 10.5%(6.4%) for K−. The spread of the corrections over
all selected bins of phase space may be visualized in Fig. 19 which also gives the distribution
of the sum of all corrections.
0
100
200
a)
0
50
100
b)
0
100
200
c)
20 10
correction [%]
01020
0
50
100
150
d)
20 10
correction [%]
01020
0
100
200
300
e)
20 10
correction [%]
010 20
0
50
100
150
f)
20 10
correction [%]
0 1020
0
20
40
60
g)
entries
entries
Figure 19: Distribution of correction for a) target reinteraction, b) trigger bias, c) absorption in
detector material, d) kaon decay, e) empty target contribution, f) binning, g) total correction
15
Page 18
6Results on double differential cross sections
6.1Data tables
The binning scheme described in Sect. 3 results in 158 data points each for K+and K−.
The corresponding cross sections are presented in Tables 2 and 3.
f(xF,pT),∆f
0.025
3.174
2.799
2.598
2.294
2.014
1.762
1.224
0.819
0.539
0.333
0.216
0.1358 6.63 0.1286 6.72 0.1357 5.34 0.1217 4.96
0.0595 6.75 0.0498 6.76
0.0194 9.08
0.0092 12.7
pT\xF
0.05
0.1
0.15
0.2
0.25
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
1.3
1.5
1.7
0.00.010.050.075
2.438
2.344
2.070
2.093
1.789
1.517
1.074
0.740
0.487
0.323
0.1
2.78
2.96
2.56
2.35
1.95
1.748
1.289
0.839
0.530
0.371
0.241
0.1412 6.75
0.0580 6.25
0.0231 8.04
0.0106 12.8
0.00354 17.3
0.125
1.87
1.758
1.813
1.603
1.379
1.243
0.912
0.617
0.410
0.2593 3.52 0.2453 3.56 0.2046 4.35 0.1756 4.84
0.1709 4.97 0.1528 4.34 0.1340 5.01 0.1130 7.62 0.1040 8.00 0.0583 7.14
0.1102 6.16 0.1019 5.55 0.0754 6.94 0.0753 8.23 0.0488 10.0 0.0372 8.47
0.0400 5.15 0.0339 6.85 0.0267 8.90 0.0200 11.0 0.0148 8.65
0.0184 8.29 0.0143 9.77 0.0118 11.7 0.0091 14.0 0.00640 12.3
0.00458 18.5 0.0055 20.6 0.00437 16.7 0.00384 19.0 0.00165 23.0
0.00257 16.0 0.00232 23.2 0.00141 30.3
7.23
4.96
6.29
5.00
6.80
4.82
3.62
4.23
3.89
4.47
5.33
2.73
3.22
2.53
2.27
2.11
1.692
1.232
0.916
5.30
4.22
5.10
5.37
5.14
5.51
4.22
5.12
2.83
2.27
2.06
1.87
3.09
2.70
2.55
3.14
3.67
4.22
5.32
2.797
2.572
2.460
2.219
1.904
1.625
1.177
0.804
0.539
0.320
0.215
3.33
2.23
1.93
1.69
1.73
1.66
1.54
2.46
3.15
4.16
5.09 0.1903 4.51 0.1812 3.98
3.54
2.62
2.28
1.98
1.94
1.92
1.56
1.82
2.10 0.4462 2.09
3.32 0.2760 2.73
2.169
2.046
1.955
1.738
1.563
1.395
0.963
0.680
4.47
2.61
2.71
2.06
2.38
1.86
1.72
2.00
0.0485 4.98
0.0184 8.03
0.00856 11.6
0.00291 13.8
0.4
pT\xF
0.05
0.1
0.15
0.2
0.25
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
1.3
1.5
1.7
0.150.20.250.3
5.51
4.20
3.21
3.11
2.85
2.75
2.19
2.40
2.82
1.60
1.469
1.396
1.390
1.313
1.057
0.809
0.574
0.385
6.47
4.09
4.02
2.96
3.44
2.76
2.46
2.59
2.96
1.2204.210.9417.940.7967.000.4755.95
0.9953.340.8436.620.7205.000.4084.56
0.842
0.666
0.493
0.339
3.24
3.06
3.04
3.64
0.729
0.540
0.394
0.269
5.29
5.19
5.00
4.22
0.546
0.450
0.392
0.208
0.143
5.00
5.00
5.00 0.2014 4.15
6.00 0.1632 4.23
7.00 0.1042 4.95
0.300
0.253
4.35
4.11
Table 2: Invariant cross section, f(xF,pT), in mb/(GeV2/c3) for K+in p+p collisions at
158 GeV/c beam momentum. The relative statistical errors, ∆f, are given in %, the transverse
momentum pTin GeV/c
16
Page 19
f(xF,pT),∆f
pT\xF
0.05
0.0 0.010.025 0.050.0750.1 0.125
1.906.062.045.042.2703.051.9113.471.5304.29 1.294 5.22 1.089 6.03
0.12.153 4.252.1514.542.0412.071.847 2.171.5402.92 1.2342.84 1.081 4.32
0.151.93 5.431.8854.931.907 1.941.7352.091.4222.521.2193.08 0.934 3.84
0.21.6004.651.6835.191.7171.691.5011.741.3332.261.0672.22 0.842 3.60
0.251.5995.571.6615.041.5222.821.2961.911.1472.220.9492.69 0.811 3.25
0.31.3014.391.1885.581.2912.491.1411.890.9972.130.8642.00 0.694 3.30
0.40.9093.510.9074.410.9052.350.7961.540.7361.670.6151.76 0.515 2.54
0.50.5884.100.5515.880.5722.970.5382.54 0.4751 2.02 0.4115 2.02 0.3734 2.62
0.60.3804.390.3783.45 0.3573.14 0.3073 2.40 0.2709 2.31 0.2263 3.21
0.7 0.235 4.620.2374 4.15 0.2038 4.32 0.1779 4.06 0.1626 2.93 0.1546 3.54
0.8 0.1502 5.350.1391 5.54 0.1356 5.34 0.1258 4.67 0.1055 4.20 0.0958 5.36
0.90.0910 7.100.0833 7.06 0.0770 6.93 0.0614 7.47 0.0687 5.29 0.0554 7.24
1.1 0.0340 6.660.0303 7.23 0.0303 6.790.0245 5.65
1.3 0.0113 9.680.0112 11.00.00758 8.00
1.50.00435 15.40.00487 16.80.00341 15.9
1.70.00211 18.80.00172 15.7
pT\xF
0.05
0.15 0.20.250.30.4 0.5
0.774 7.78
0.10.759 4.520.514 4.540.290 7.500.208 11.4 0.1318 7.14 0.0323 30.7
0.15 0.7424.75
0.20.709 3.370.478 3.240.2996.110.217 7.72
0.250.647 3.96
0.30.5973.000.3813.150.2435.460.1837.46 0.0966 4.77 0.0226 11.0
0.40.4242.67 0.2623 3.63 0.2125.06 0.1268 7.87
0.50.3022 2.90 0.2044 3.64 0.1415 5.88 0.0936 8.14 0.0389 5.84 0.0172 9.78
0.60.1900 3.36 0.1524 3.91 0.0957 6.08 0.0706 8.41
0.70.1306 3.81 0.0921 4.86 0.0553 7.57 0.0445 9.76 0.0165 7.64 0.0110 10.4
0.80.0780 4.80 0.0600 5.63 0.0381 8.89 0.0252 12.4
0.90.0480 5.98 0.0402 6.72 0.0257 9.77 0.0187 13.3 0.00878 9.26 0.00363 16.0
1.10.0191 6.32 0.01204 8.14 0.00875 10.8 0.00736 13.3 0.00246 16.2 0.00106 27.7
1.30.00805 10.2 0.00578 10.5 0.00302 16.9 0.00163 27.8 0.00080 26.5
1.5 0.00271 17.0 0.00198 18.5 0.00189 19.9 0.00110 31.4
1.70.00102 18.30.00054 30.3
Table 3: Invariant cross section, f(xF,pT), in mb/(GeV2/c3) for K−in p+p collisions at
158 GeV/c beam momentum. The relative statistical errors, ∆f, are given in %, the transverse
momentum pTin GeV/c
17
Page 20
6.2 Interpolation scheme
As in the preceding publications concerning p+p and p+C interactions [1,2,32] a two
dimensional interpolation based on a multistep recursive method using eyeball fits has been
applied. The distribution of the differences of the measured points with respect to this interpo
lation, divided by the given statistical error should be Gaussian with mean zero and variance
unity if the interpolation is biasfree and if the estimation of the statistical errors, see Sect. 4.5
above, is correct. The corresponding distributions shown in Fig. 20 comply with this expecta
tion.
Entries
f
∆
/ ∆
42024
0
5
10
15
20
25
= 0.93
σ
mean = 0.04
a)
+
K
f
∆
/ ∆
4 2024
0
5
10
15
20
25
= 0.88
σ
mean = 0.06
b)

K
Figure 20: Difference ∆ between the measured invariant cross sections and the corresponding
interpolated values divided by the experimental uncertainty ∆f for a) K+and b) K−
As tofirst orderthe8first neighboursand tothesecondthe24second neighboursto each
data point contribute to the establishment of the interpolation, a reduction of the local statistical
fluctuations of a factor of 3 to 4 may be expected. The authors therefore advise to use the data
interpolation which is available under [33] for data comparison and analysis purposes. On the
pointbypoint level, the statistical error of the interpolated cross sections has been estimated as
the mean value of the statistical errors of each measured point plus the 8 surrounding points in
the pT/xFplane, divided by the (conservative) factor of 2. The systematic uncertainties are of
course not touched by this procedure, in addition they are of mostly nonlocal origin.
6.3Dependence of invariant cross sections on xFand pT
Shapes of the invariant cross sections as functions of pTand xFare shown in Figs. 21
and 22 including the data interpolation presented above. In order to clearly demonstrate the
shape evolution and to avoid overlap of plots and error bars, subsequent pTdistributions have
been multiplied by factors of 0.5 (Fig. 21).
6.4Rapidity and transverse mass distributions
As in the preceding publications [1,2,32] data and interpolation are also shown as func
tions of rapidity at fixed pTin Fig. 23.
18
Page 21
)]
3
/c
2
f [mb/(GeV
[GeV/c]
T
p
0 0.511.52
7
10
5
10
3
10
1
10
10
= 0.0
F
x
0.01
0.025
0.05
0.075
0.1
0.125
0.15
0.2
0.25
0.3
0.4
X
+
K
→
pp
a)
[GeV/c]
T
p
0 0.51 1.52
= 0.0
F
x
0.01
0.025
0.05
0.075
0.1
0.125
0.15
0.2
0.25
0.3
0.4
0.5
X

K
→
pp
b)
Figure 21: Double differential invariant cross section f(xF,pT) [mb/(GeV2/c3)] as a function
of pTat fixed xFfor a) K+and b) K−produced in p+p collisions at 158 GeV/c beam momen
tum. The distributions for different xF values are successively scaled down by 0.5 for better
separation. The lines show the result of the data interpolation, Sect. 6.2
19
Page 22
)]
3
/c
2
f [mb/(GeV
F
x
00.2 0.4
3
10
2
10
1
10
1
10
= 0.05 GeV/c
0.1
0.15
0.2
0.25
0.3
0.4
0.5
T
p
0.6
0.7
0.8
0.9
1.1
1.3
1.5
1.7
X
+
K
→
pp
a)
F
x
00.20.4
= 0.05 GeV/c
0.1
0.15
0.2
0.25
0.3
0.4
0.5
0.6
0.7
T
p
0.8
0.9
1.1
1.3
1.5
1.7
X

K
→
pp
b)
Figure 22: Double differential invariant cross section f(xF,pT) [mb/(GeV2/c3)] as a function of
xFat fixed pTfor a) K+and b) K−produced in p+p collisions at 158 GeV/c beam momentum.
The lines show the result of the data interpolation, Sect. 6.2
20
Page 23
)]
3
/c
2
f [mb/(GeV
y
012
3
10
2
10
1
10
1
10
= 0.05 GeV/c
0.1
0.15
0.2
0.25
0.3
0.4
T
p
0.5
0.6
0.7
0.8
0.9
1.1
1.3
1.5
1.7
X
+
K
→
pp
a)
y
012
= 0.05 GeV/c
0.1
0.15
0.2
0.25
0.3
0.4
0.5
0.6
0.7
T
p
0.8
0.9
1.1
1.3
1.5
1.7
X

K
→
pp
b)
Figure 23: Double differential invariant cross section f(xF,pT) [mb/(GeV2/c3] as a function of
y at fixed pTfor a) K+and b) K−produced in p+p collisions at 158 GeV/c beam momentum.
The lines show the result of the data interpolation, Sect. 6.2
21
Page 24
)]
3
/c
2
f [mb/(GeV
]
2
[GeV/c
K
 m
T
m
00.51
3
10
2
10
1
10
1
a)
y = 0.0
+
K
]
2
[GeV/c
K
 m
T
m
00.51
b)
y = 0.0

K
Figure 24: Invariant cross section as a function of mT− mKfor a) K+and b) K−produced at
y = 0.0. The lines show the result of the data interpolation, Sect. 6.2
Transverse mass distributions at xF= y = 0, with mT =
Fig. 24 again including the data interpolation. The corresponding dependence of the inverse
slopes of these distributions on mT−mKis shown in Fig. 25 together with the results from the
data interpolation. The local slope values are defined by three successive data points.
K+and K−show a similar behaviour of the inverse slope parameters which fall from
valuesaround180 MeV at lowmT−mKto aminimumof150MeV at mT−mK∼0.05 GeV/c2
(pT∼ 0.220 GeV/c), see also results from ISR (Fig. 74). They then rise steadily towards higher
mTand reach 180 MeV at pT∼ 0.6 (0.9) GeV/c and 200 MeV at pT∼ 1.0 (1.8) GeV/c for K+
and K−, respectively. These trends resemble the ones observed for pions [1].
?m2
K+ p2
T, are presented in
inverse slope T [MeV]
]
2
[GeV/c
K
 m
T
m
0 0.51
0
100
200
300
400
a)
y = 0.0
+
K
]
2
[GeV/c
K
 m
T
m
00.51
b)

K
Figure 25: Local inverse slope of the mTdistribution as a function of mT− mKfor a) K+and
b) K−. The lines correspond to the data interpolation, Sect. 6.2
7 Particle ratios
The present data on charged kaon production offer, together with the already available
pion [1] and baryon [2] cross sections with similarphase space coverageand precision, a unique
possibility to study particle ratios, in particular their evolution with transverse momentum and
22
Page 25
xF.ThissectionwillthereforenotonlydealwithK+/K−butwillalsoaddress K/π and K/baryon
ratios.
7.1K+/K−ratios
The ratio of the inclusive K+and K−cross sections,
RK+K− = f(K+)/f(K−)
(10)
is shown in Fig. 26 as a function of xFat fixed pTand in Fig. 27 as a function of pTat fixed
values of xF.
= 0.05 GeV/c
T
p = 0.1 GeV/c
T
p = 0.15 GeV/c
T
p = 0.2 GeV/c
T
p
= 0.25 GeV/c
T
p = 0.3 GeV/c
T
p = 0.4 GeV/c
T
p = 0.5 GeV/c
T
p
= 0.6 GeV/c
T
p = 0.7 GeV/c
T
p = 0.8 GeV/c
T
p = 0.9 GeV/c
T
p
00.1 0.20.30.4
= 1.1 GeV/c
T
p
00.1 0.20.30.4
= 1.3 GeV/c
T
p
00.1 0.20.30.4
= 1.5 GeV/c
T
p
00.1 0.20.30.4
= 1.7 GeV/c
T
p

K
+
K
R

K
+
K
R

K
+
K
R

K
+
K
R
F
x
F
x
F
x
F
x
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
Figure 26: RK+K− as a function of xFat fixed pT. The lines show the result of the data interpo
lation, Sect. 6.2
In each panel the corresponding ratio of the data interpolations, Sect. 6.2, is superim
posed to the data points as a solid line. The basic features of the data may be described as a
steady increase of RK+K− over the available xFrange by about a factor of three (Fig. 26) with
some structure visible at certain xFand pTvalues. The pTdependence (Fig. 27) reveals a more
detailed evolution. The increase of RK+K− in the interval 0 < pT < 1.7 GeV/c which amounts
to about 60% at low xFflattens out in the xFrange 0.1 – 0.2 to only 20% before it increases
23
Page 26
= 0.0
F
x = 0.01
F
x = 0.025
F
x = 0.05
F
x
= 0.075
F
x = 0.1
F
x = 0.125
F
x = 0.15
F
x
0.5
p
11.5
= 0.2
F
x
0.5
p
1 1.5
= 0.25
F
x
0.5
p
1 1.5
= 0.3
F
x
0.5
p
11.5
= 0.4
F
x

K
+
K
R

K
+
K
R

K
+
K
R
[GeV/c]
T
[GeV/c]
T
[GeV/c]
T
[GeV/c]
T
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
Figure 27: RK+K− as a function of pTat fixed xF. The lines show the result of the data interpo
lation, Sect. 6.2
again towards higher xF. This may be visualized in Fig. 28 where the ratios of the interpo
lated cross sections are shown as a function of pTfor several xFvalues on an enlarged vertical
scale. Fig. 28b gives an estimate of the statistical uncertainty of RK+K− to be expected for data
interpolation, characterized by the hatched area around the nominal values.

K
+
K
R
[GeV/c]
T
p
00.51 1.5
b)
= 0.0
F
= 0.2
F
= 0.25
F
x
x
x
[GeV/c]
T
p
00.51 1.5
1
2
3
4
= 0.0
= 0.05
= 0.1
= 0.15
= 0.2
= 0.25
F
F
F
F
F
F
x
x
x
x
x
x
a)
Figure 28: a) RK+K− for the data interpolation as a function of pT for different xF; b) Error
bands expected for data interpolation
24
Page 27
7.2K/π ratios
TheK/π ratios shownheremakeuseofthepiondataand thecorrespondinginterpolation
published in [1]. The ratios of the invariant inclusive cross sections
RK+π+ = f(K+)/f(π+)
RK−π− = f(K−)/f(π−)
(11)
(12)
are presented in Figs. 29 to 34.
RK+π+ is shown in Fig. 29 as a function of pTfor fixed xFand in Fig. 30 as a function
of xFfor fixed pT.
= 0.0
F
x = 0.01
F
x = 0.05
F
x = 0.1
F
x
0.5
[GeV/c]
T
11.5
= 0.15
F
x
0.5
p
1 1.5
= 0.2
F
x
0.5
p
1 1.5
= 0.25
F
x
0.5
p
11.5
= 0.3
F
x
+
π
+
K
R
+
π
+
K
R
p [GeV/c]
T
[GeV/c]
T
[GeV/c]
T
0.4
0.2
0
0.4
0.2
0
Figure 29: RK+π+ as a function of pTat fixed xF. The lines show the result of the data interpo
lation, Sect. 6.2
= 0.1 GeV/c
T
p = 0.3 GeV/c
T
p = 0.5 GeV/c
T
p = 0.7 GeV/c
T
p
00.2
x
0.4
= 0.9 GeV/c
T
p
00.2
x
0.4
= 1.1 GeV/c
T
p
00.20.4
= 1.3 GeV/c
T
p
00.2 0.4
= 1.7 GeV/c
T
p
+
π
+
K
R
+
π
+
K
R
FFF
x
F
x
0.4
0.2
0
0.4
0.2
0
Figure 30: RK+π+ as a function of xFat fixed pT. The lines show the result of the data interpo
lation, Sect. 6.2
Here the salient features are the strong increase with pT which is rather independent
on xFand reaches values of about 6 relative to low pTat 1.7 GeV/c, and the rather small xF
dependence with a slight increase at low pT and a comparable small decrease in the high pT
region. These features are again shown in the composite Fig. 31 where the pTdependence of
RK+π+ from the interpolated data is plotted for the full range of xFvalues.
25
Page 28
[GeV/c]
T
p
00.511.5
+
π
+
K
R
0
0.1
0.2
0.3
0.4
= 0.0
F
= 0.1
F
= 0.2
F
= 0.3
F
= 0.4
F
x
x
x
x
x
Figure 31: RK+π+ as a function of pTfor different xF
In Fig. 31 the ”crossover” point at pT∼ 0.5–0.7 GeV/c where the full relative variation
of RK+π+ with xFis on the level of only 20% of the ratio, and the practically parallel evolution
of RK+π+ with pTfor different xFover a wide range of transverse momentum should be pointed
out.
RK−π− is shown in Fig. 32 as a function of pTat fixed xFand in Fig. 33 as a function of
xFfor fixed pT.
= 0.0
F
x = 0.01
F
x = 0.05
F
x = 0.1
F
x
0.5
[GeV/c]
T
11.5
= 0.15
F
x
0.5
p
1 1.5
= 0.2
F
x
0.5
p
11.5
= 0.25
F
x
0.5
p
1 1.5
= 0.3
F
x
π

K
R
π

K
R
p [GeV/c]
T
[GeV/c]
T
[GeV/c]
T
0.2
0.1
0
0.2
0.1
0
Figure 32: RK−π− as a function of pTat fixed xF. The lines show the result of the data interpo
lation, Sect. 6.2
Also for RK−π− a strong increase with pTand the independence on xFfor low pTfol
lowed by a decrease with xFat high pTare evident. This is visualized in the composite Fig. 34
where the pTdependence for several xFvalues is plotted for the interpolated data values.
Again a ”crossover” point in pT with a practically complete xF independence, for
RK−π− at pT∼ 0.3 GeV/c should be mentioned, together with the more pronounced decrease at
higher pT. A general remark concerns the low pTregions of Figs. 29, 31, 32 and 34. The rapid
variation of the K/π ratios below pT ∼ 0.2 GeV/c with some minima at pT ∼ 0.15 GeV/c are
due to the structure of the π+and π−cross sections observed in this region [1]. This structure
is more pronounced for π+than for π−and has been explained by resonance decay [1,34].
26
Page 29
= 0.1 GeV/c
T
p = 0.3 GeV/c
T
p = 0.5 GeV/c
T
p = 0.7 GeV/c
T
p
00.2
x
0.4
= 0.9 GeV/c
T
p
00.2
x
0.4
= 1.1 GeV/c
T
p
00.20.4
= 1.3 GeV/c
T
p
0 0.20.4
= 1.7 GeV/c
T
p
π

K
R
π

K
R
FFF
x
F
x
0.2
0.1
0
0.2
0.1
0
Figure 33: RK−π− as a function of xFat fixed pT. The lines show the result of the data interpo
lation, Sect. 6.2
[GeV/c]
T
p
00.51 1.5
π

K
R
0
0.05
0.1
0.15
0.2
0.25
= 0.0
F
= 0.1
F
= 0.2
F
= 0.3
F
= 0.4
F
x
x
x
x
x
Figure 34: RK−π− as a function of pTfor different xF
7.3K/baryon ratios
The K/baryon ratios shownbelowuse thenew data on proton and antiprotonproduction
published in [2]. The ratios of the invariant inclusive cross sections
RK+p= f(K+)/f(p)
RK−p= f(K−)/f(p)
(13)
(14)
are presented in Figs. 35 to 41.
RK+pis shown in Fig. 35 as a function of pTfor fixed xFand in Fig. 36 as a function of
xFfor fixed pT.
Fig. 35 indicates a strong, rapidly decreasing K+component at low pTand xF ? 0.15,
superimposed on an almost pTindependent contribution which shows a marked decrease with
increasing xFbut also a slight increase with pTat xF> 0.2. This corresponds to the strong xF
dependence at low pT in Fig. 36 which flattens out rapidly with increasing pT. The compos
ite Fig. 37 joins these trends using the ratio of the data interpolations as a function of pT for
27
Page 30
= 0.0
F
x = 0.05
F
x = 0.1
F
x = 0.15
F
x
0.5
[GeV/c]
T
1 1.5
= 0.2
F
x
0.5
p
11.5
= 0.25
F
x
0.5
p
11.5
= 0.3
F
x
0.5
p
1 1.5
= 0.4
F
x
p
+
K
R
p
+
K
R
p [GeV/c]
T
[GeV/c]
T
[GeV/c]
T
1.5
1
0.5
0
1.5
1
0.5
0
Figure 35: RK+pas a function of pTat fixed xF. The lines show the result of the data interpola
tion, Sect. 6.2
= 0.1 GeV/c
T
p = 0.3 GeV/c
T
p = 0.5 GeV/c
T
p = 0.7 GeV/c
T
p
0 0.2
x
0.4
= 0.9 GeV/c
T
p
00.2
x
0.4
= 1.1 GeV/c
T
p
0 0.2
x
0.4
= 1.3 GeV/c
T
p
00.2
x
0.4
= 1.7 GeV/c
T
p
/p
+
K
R
/p
+
K
R
FFFF
1.5
1
0.5
0
1.5
1
0.5
0
Figure 36: RK+pas a function of xFat fixed pT. The lines show the result of the data interpola
tion, Sect. 6.2
different xFvalues.
p
+
K
R
[GeV/c]
T
p
00.511.5
b)
= 0.0
= 0.1
= 0.2
= 0.3
= 0.4
F
F
F
F
F
x
x
x
x
x
[GeV/c]
T
p
0123
0
0.5
1
1.5
= 0.0
= 0.05
= 0.1
= 0.15
= 0.2
= 0.25
= 0.3
= 0.4
F
F
F
F
F
F
F
F
x
x
x
x
x
x
x
x
a)
Figure 37: a) RK+pfor the data interpolation as a function of pTfor different xF; b) Error bands
expected for data interpolations
28
Page 31
RK+pseems to converge towards high pT to an xF independent value of about 0.4 –
0.5 as indicated in Fig. 37 by the dashed extrapolated lines for the different xF values. This
is reminiscent of a similar behaviour for the p/?π? ratio pointed out in [2]. As the point of
convergence seems to lie close to pT ∼ 3 GeV/c it is tempting to use the available data at this
transverse momentum from different√s, although the detailed study of the sdependence of
RK+pis outside the scope of this work. The analysis of the existing data at pT= 3 GeV/c and
xF= 0 from Serpukhov energy [11] via Fermilab [12] to ISR [15–17,20–22], Fig. 38, shows
indeed consistency within errors with the value from the extrapolation shown above, indicating
at the same time the very strong sdependence of this particle ratio at high pT.
[GeV]s
0204060
p
+
K
R
0
0.5
1
1.5
2
= 3 GeV/c
T
= 0
F
p
x
Figure 38: sdependence of RK+pat pT= 3 GeV/c and xF= 0. The open circle corresponds to
the NA49 extrapolation, Fig. 37
It should be remarked here that the Fermilab data have been corrected for a systematic
effect of 20% concerning the proton yields discussed in [2] and all ISR ratios by 10% to account
for the expected amount of proton feeddown from strange baryons.
RK−pis shown in Fig. 39 as a function of pTfor fixed xFand in Fig. 40 as a function of
xFfor fixed pT.
= 0.0
F
x = 0.05
F
x = 0.1
F
x = 0.15
F
x
0.5
[GeV/c]
T
1 1.5
= 0.2
F
x
0.5
p
1 1.5
= 0.25
F
x
0.5
p
11.5
= 0.3
F
x
0.5
p
1 1.5
= 0.4
F
x
p

K
R
p

K
R
p [GeV/c]
T
[GeV/c]
T
[GeV/c]
T
10
5
0
10
5
0
Figure 39: RK−pas a function of pTat fixed xF. The lines show the result of the data interpola
tion, Sect. 6.2
29
Page 32
= 0.1 GeV/c
T
p = 0.3 GeV/c
T
p = 0.5 GeV/c
T
p = 0.7 GeV/c
T
p
00.2
x
0.4
= 0.9 GeV/c
T
p
00.2
x
0.4
= 1.1 GeV/c
T
p
00.2
x
0.4
= 1.3 GeV/c
T
p
00.2
x
0.4
= 1.5 GeV/c
T
p
p
/

K
R
p /

K
R
FFFF
10
5
0
10
5
0
Figure 40: RK−pas a function of xFat fixed pT. The lines show the result of the data interpola
tion, Sect. 6.2
As for RK+pthe sizeable pTdependence at low xFflattens out at medium xF, 0.15 <
xF< 0.25, and reappears towards xF= 0.4. The xFdependence, Fig. 40, is very different from
the one of RK+p. There is no strong enhancement at low xF, RK−pbeing rather independent on
xFup to xF∼ 0.3. Beyond this value the ratio increases rapidly towards values between 5 and
6 at the maximum accessible xF. Fig. 41 shows these trends using the ratio of the interpolated
data as a function of pTfor different xF.
p

K
R
[GeV/c]
T
p
0 0.511.5
b)
= 0.0
= 0.3
F
F
x
x
[GeV/c]
T
p
0 0.51 1.5
1.5
2
2.5
3
3.5
4
= 0.0
= 0.05
= 0.1
= 0.15
= 0.2
= 0.25
= 0.3
F
F
x
x
x
x
x
x
x
F
F
F
F
F
a)
Figure 41: a) RK−pfor the data interpolation as a function of pTfor different xF; b) Error bands
expected for data interpolations
The small structures described above are clearly visible, together with the strong in
crease at xF> 0.25 and a minimum at pTvalues between 0.9 and 1.1 GeV/c.
8 Comparison to Fermilab data
In a first step of data comparison, the NA49 data will be compared to the existing,
double differential cross sections at neighbouring energies in order to control data consistency
30
Page 33
with only small necessary corrections for s dependence. A wider range of comparisons ranging
from kaon threshold to RHIC and collider energies will be performed in Sect. 10 below. For
the case of kaons all comparisons are facilitated by the absence of feeddown corrections from
weak decays of strange particles.
8.1 The Brenner et al. data [13]
This experiment which has shown a good agreement on the level of the double differ
ential cross sections for pions [1] and baryons [2], offers 37 data points for K+and 32 points
for K−at the two beam momenta of 100 and 175 GeV/c. The average statistical errors of these
data are unfortunately rather large for the kaon samples, with about 25% for K+and 40% for
K−. This is shown in the error distributions of Fig. 42, panels a) and d). Although the√s values
at the two beam energies are, with 13.5 and 18.1 GeV, close to the NA49 energy, an upwards
correction of 8% (12%) at the lower energy and a downwards correction of 2% (5%) at the
higher energy has been applied for K+and K−, respectively, see Sect. 10 for a more detailed
discussion of s dependence.
0 204060
0
2
4
6
8
a)
+
K
40 20
8
e)
020 4060 80
0
2
4
6
8
10
= 17.0
σ
mean = 1.7
b)
+
K
202
0
5
10
= 1.04
σ
mean = 0.07
c)
+
K
050100150
0
5
10
d)

K
500
∆
50100
0
2
4
6
= 31.5
σ
mean = 18.6

K
202
0
5
10
= 0.86
σ
mean = 0.29
f)

K
Entries
Entries
[%]
∆
σ
[%]
∆
σ / ∆
Figure 42: Statistical analysis of the difference between the measurements of [13] and NA49
for K+(upper three panels) and K−(lower three panels): a) and d) error of the difference of
the measurements; b) and e) difference of the measurements; c) and f) difference divided by the
error
The statistical analysis ofthe differences between the Brenner et al. data and the interpo
lated NA49 results is presented in Fig. 42. Although the relative differences, dominated by the
statisticalerrors of [13], are very sizeable, see panels b)and e), the differences normalized to the
given statistical errors, panels c) and f) show reasonable agreement between the two data sets,
31
Page 34
in particular for K+where the normalized differences are centered at ∆/σ = 0 with the expected
variance of unity. The K−show a positive offset of 0.3 standard deviations which corresponds
to an average difference of 19%.
A visualization of the Brenner data with respect to the interpolated NA49 results and
their distribution in the xFand pTvariables is given in Fig. 43.
)]
3
/c
2
f [mb/(GeV
)]
3
/c
2
f [mb/(GeV
[GeV/c]
T
p
F
x
00.2 0.40.6 0.8
5
10
4
10
3
10
2
10
1
10
1
10
2
10
a)
+
K
= 0.2
F
x
0.3
0.4
100 GeV/c
175 GeV/c
0 0.20.4
7
10
5
10
3
10
1
10
10
2
10
b)
+
K
= 0.1 GeV/c
T
0.15
0.2
0.25
0.3
p
0.4
0.5
0.75
0.85
0 0.20.40.6 0.8
5
10
4
10
3
10
2
10
1
10
1
10
2
10
c)

K
100 GeV/c
175 GeV/c
= 0.2
0.3
0.4
0.5
F x
00.20.4
7
10
5
10
3
10
1
10
10
2
10
d)

K
= 0.1 GeV/c
T
0.15
0.2
0.25
0.3
0.4
p
0.5
0.75
0.85
Figure 43: Comparison of invariantcross section between NA49 (lines)and measurements from
[13] at 100 (full circles) and 175 GeV/c (open circles) for K+as a function of a) pTat fixed xF
and b) xFat fixed pT, and for K−as a function of c) pTat fixed xFand d) xFat fixed pT. The
data were successively divided by 4 for better separation
Taking into account the comparison of all measured particle species for the two experi
ments [1,2] it may be stated that a rather satisfactory overall agreement, within the limits of the
respective systematic and statistical errors, has been demonstrated.
32
Page 35
8.2The Johnson et al. data [14]
This experimentgives 40 data points for K+and 50 pointsfor K−withinthe range of the
NA49 data obtained at 100, 200 and 400 GeV/c beam momentum. For comparison purposes the
data have been corrected to 158 GeV/c beam momentum using the sdependence established in
Sect. 10 below. The distribution of the relative statistical errors is shown in Fig. 44 panel a) for
K+and panel d) for K−, with mean values of 12% and 9%, respectively. This is substantially
below the errors of [13].
010203040
0
5
10
15
a)
+
K
200204060
0
5
10
15
= 14.9
σ
mean = 23.5
b)
+
K
505
0
5
10
15
20
= 1.71
σ
mean = 2.47
c)
+
K
0 1020
σ
3040
0
5
10
15
d)

K
50050 100
0
5
10
= 30.0
σ
mean = 10.5
e)

K
10 505 10
0
5
10
15
= 3.01
σ
mean = 0.99
f)

K
Entries
Entries
[%]
∆
[%]
∆
∆
σ / ∆
Figure 44: Statistical analysis of the difference between the measurements of [14] and NA49
for K+(upper three panels) and K−(lower three panels): a) and d) error of the difference of
the measurements; b) and e) difference of the measurements; c) and f) difference divided by the
error
The statistical analysis of the differences with respect to the interpolated cross sections
of NA49 is also given in Fig. 44 in terms of the distribution of the relative difference ∆, panels
b),e) and of the difference normalized to the statistical error ∆/σ, panels c) and f). Two main
features are apparent from this comparison: an upwards shift of about 23% (10%) correspond
ing to 2.5 (1.0) standard deviations and large fluctuations corresponding to 1.7 (3.0) standard
deviations for K+and K−, respectively. As similar observations have been made for pions [1]
and baryons [2] one may state that a general offset of 10 – 20% seems to be present which is
compatible with the normalization uncertainty given in [14]. The fact that the proton data show
a smaller offset might be connected with their xFcoverage which is mostly at large negativexF
(low lab momenta). On the other hand, the underestimation of the point by point fluctuations
by a factor of 2 to 4 with respect to the claimed statistical errors, for all particle species, has to
remain unresolved.
33
Page 36
The phase space distribution of the data of [14] is shown in Fig.45 as a function of xF
at fixed values of pTin comparison with the interpolated NA49 cross sections.
)]
3
/c
2
f [mb/(GeV
F
x
00.10.2 0.30.4
4
10
3
10
2
10
1
10
1
10
a)
+
K
= 0.25 GeV/c
0.5
0.75
1.0
T
p
F
x
00.2 0.4
4
10
3
10
2
10
1
10
1
10
b)

K
100 GeV/c
200 GeV/c
400 GeV/c
= 0.25 GeV/c
T
0.5
0.75
1.0
p
Figure 45: Comparison of invariantcross section between NA49 (lines)and measurements from
[14] at 100 (full circles), 200 (open circles) and 400 GeV/c (full triangles) as a function of xF
at fixed pTfor a) K+and b) K−. The data were successively divided by 3 for better separation
8.3 The Antreasyan et al. data [12]
It is only the lowpTpart of this experiment which can be compared to the NA49 data,
at xF close to 0. Due to the fact that the spectrometer of [12] was set to a constant lab angle
for all beam energies and particle species, the given cross sections have to be compared at their
proper xFvalues as given in Table 4, see also the corresponding arguments in [2].
pT[GeV/c]
pbeam[GeV/c]
√s [GeV]
xF
RK+
RK−
xF
RK+
RK−
200
19.3
0.0054
0.826±0.12
0.966±0.12
0.0302
0.796±0.05
0.791±0.06
300
23.7
0.011
1.026±0.16
1.217±0.18
0.031
1.080±0.08
1.240±0.06
400
27.3
0.020
1.110±0.20
1.164±0.18
0.020
1.260±0.12
1.616±0.14
0.77
1.54
Table 4: Offset in xF at different√s and pT. The cross section ratio RK± between the data
from [12] and NA49.
The cross section ratios RK+ and RK− are shown in Fig. 46 as a function of√s at fixed
pT, togetherwith thesdependenceextracted in Sect. 10below from dataat xF= 0 at Serpukhov
energy [11] and ISR energy [21,22].
Evidently the data [12] comply, within their sizeable statistical errors, with the s
dependence as established by the other experiments. However, three of the four points at
34
Page 37
K
R
[GeV]s
0102030
b)

K
= 0.77 GeV/c
T
p
= 1.54 GeV/c
T
p
[GeV]s
010 2030
0
1
2
a)
+
K
= 0.77 GeV/c
T
p
= 1.54 GeV/c
T
p
Figure 46: The cross section ratios between the data from [12] and NA49 as a function of√s
for two values of pT for a) K+and b) K−. In both of the panels the NA49 point is indicated
with full triangle. The full and dashed lines represent the result of the sdependence at xF= 0
established in Sect. 10 below at pT= 0.77 and 1.54 GeV/c, respectively
200 GeV/c beam momentum are low by about two standard deviations. This would, by us
ing the data [12] alone to establish the sdependence, lead to a large underestimation of the
kaon yields at lower s. See also the discussion in [2] for baryons.
8.4Comparison of particle ratios
As systematic effects tend in general to be reduced in particle ratios, it is interesting to
also look at theconsistency of the corresponding ratios from [12–14] with the NA49 data shown
in Sect. 7 of this paper. This is shown in Fig. 47 for RK+K− ratios, in Fig. 48 for RK±π± and in

K
+
K
R
F
x
00.1 0.2 0.30.4
0
20
40
60
b)
= 1.0 GeV/c
T
p
0.75
0.5
0.3
0.25
[13] [14]
100 GeV/c
200 GeV/c
100 GeV/c
175 GeV/c
[GeV/c]
T
p
00.51 1.5
0
20
40
a)
[12]
200 GeV/c
300 GeV/c
400 GeV/c
F
x
0.4
0.3
0.2
0.0
Figure 47: Comparison of RK+K− between [12] (triangles), [13] (circles), [14] (squares) and
NA49 (lines) as a function of a) xF and b) pT. The data were successively shifted by 10 for
better separation
35
Page 38
+
π
+
K
R
π

K
R
[GeV/c]
T
p
F
x
0
0.5
1
a)
F
x
0.4
0.3
0.2
0.0
[13]
[12]
200 GeV/c
300 GeV/c
400 GeV/c
100 GeV/c
175 GeV/c
0
0.5
1
1.5
b)
= 1.0 GeV/c
T
p
0.75
0.5
0.4
0.3
0.25
0.2
[14]
100 GeV/c
200 GeV/c
0 0.51 1.5
0
0.5
1
c)
F
x
0.5
0.4
0.3
0.2
0.0
0 0.20.4
0
0.5
1
1.5
d)
= 1.0 GeV/c
T
p
0.75
0.5
0.4
0.3
0.25
0.2
Figure 48: Comparison between [12] (triangles), [13] (circles), [14] (squares) and NA49 (lines)
of RK+π+ as a function of a) pTand b) xFand RK−π− as a function of c) pTand d) xF. The data
were successively shifted by 0.2 for better separation
Fig. 49 for K/baryon ratios.
8.5Conclusion from data comparison at Fermilab energies
In conclusion of the detailed comparisons in the Fermilab/SPS energy range shown
above it may be stated that a mutually consistent picture for kaon production from several
independent experiments has been established, with the exception of some offsets in the ab
solute cross section especially for [12] and [14]. These offsets tend to cancel in the particle
ratios RK+K− for both [12] and [14]. The ratios RKπand RKpare consistent for [13] and [14]
within their statistical uncertainties, whereas for [12] the systematic effects discussed in [2] for
36
Page 39
p
+
K
R
p

K
R
[GeV/c]
T
p
F
x
0
2
4
a)
F
x
0.4
0.3
0.2
0.0
[13]
[12]
200 GeV/c
300 GeV/c
400 GeV/c
100 GeV/c
175 GeV/c
0
2
4
6
8
b)
p = 0.75 GeV/c
T
0.5
0.4
0.3
0.25
0.2
[14]
100 GeV/c
200 GeV/c
0 0.511.5
0
10
20
30
c)
F
x
0.4
0.3
0.2
0.0
0 0.20.4
0
10
20
30
40
50
d)
= 0.75 GeV/c
T
p
0.5
0.4
0.3
0.25
0.2
Figure 49: Comparison between [12] (triangles), [13] (circles), [14] (squares) and NA49 (lines)
of RK+pas a function of a) pTand b) xFand RK−pas a function of c) pTand d) xF. The data
were successively shifted by 1.2 for RK+pand by 6 for RK−pfor better separation
baryons and in Sect. 8.3 for kaons persist for RKπand RKp. What is also important to note is the
apparent absence of systematic deviations as a function of kinematic variables xFand pT. This
lends, as none of the existing experiments has on its own sufficient phase space coverage, some
confidence to the establishment of pTintegrated and total yields from the NA49 measurements
alone, as discussed below.
9 Integrated data
In a first step the data interpolation, Sect. 6.2, will be used to perform an integration
over transverse momentum. In a second step the total charged kaon yields will be determined.
37
Page 40
These can be used, in conjunction with the total pion and baryon yields published before [1,2]
to control the total charged multiplicity with respect to the precision data from bubble chamber
experiments.
9.1
pTintegrated distributions
The pTintegrated noninvariant and invariant kaon yields are defined by:
dn
dxF
=
π
σinel
?
π
σinel
√s
2
?
f
Edp2
T
F =f dp2
T
(15)
dn
dy=
?
f dp2
T
with f = E · d3σ/dp3, the invariant double differential cross section. The integrations are per
formed numerically using the twodimensional data interpolation (Sect. 6.2) which is available
in steps of 0.05 GeV/c in transverse momentum.
K+
∆
K−
∆
K+
dn/dy dn/dy
K−
xF
0.0
0.01 0.6688 1.54 0.8417 1.49 0.4165 0.78 0.2435 1.39 0.4760 1.90 0.6096 1.78 0.4007 0.87 0.2228 1.60 0.2 0.06597 0.04693
0.025 0.6648 0.87 0.7985 0.78 0.4208 0.53 0.2480 1.04 0.4644 0.82 0.5666 0.76 0.4053 0.45 0.2277 0.91 0.4 0.06496 0.04536
0.05 0.6344 0.73 0.6633 0.67 0.4343 0.40 0.2629 0.86 0.4286 0.66 0.4547 0.63 0.4198 0.45 0.2427 1.03 0.6 0.06258 0.04216
0.075 0.5906 0.63 0.5260 0.59 0.4509 0.39 0.2814 0.76 0.3745 0.68 0.3364 0.72 0.4378 0.35 0.2627 0.70 0.8 0.05910 0.03819
0.10.5374 0.64 0.4077 0.61 0.4657 0.42 0.2990 0.91 0.3210 0.70 0.2449 0.68 0.4542 0.46 0.2815 0.99 1.0 0.05458 0.03339
0.125 0.4923 0.81 0.3219 0.80 0.4776 0.47 0.3136 0.89 0.2730 0.90 0.1792 0.90 0.4690 0.46 0.2989 0.88 1.2 0.04904 0.02803
0.15 0.4449 0.87 0.2542 0.86 0.4881 0.49 0.3261 1.02 0.2267 1.05 0.1298 1.04 0.4826 0.63 0.3156 1.30 1.4 0.04328 0.02227
0.20.3614 1.07 0.1635 1.06 0.5037 0.69 0.3449 1.58 0.1568 1.31 0.07101 1.22 0.5006 0.71 0.3369 1.44 1.6 0.03680 0.01677
0.25 0.2965 1.79 0.1104 1.70 0.5127 0.94 0.3551 1.77 0.1041 1.90 0.03880 2.10 0.5080 1.08 0.3460 2.19 1.8 0.03030 0.01182
0.30.2373 1.90 0.07491 1.90 0.5184 0.97 0.3620 1.98 0.07112 2.53 0.02248 2.53 0.5059 1.44 0.3445 2.83 2.0 0.02389 0.00774
0.40.1481 1.44 0.03569 1.43 0.5259 0.96 0.3705 1.92 0.03296 2.51 0.007959 2.51 0.4933 1.49 0.3305 2.88 2.2 0.01788 0.00485
0.50.01370 5.36 0.002667 5.37 0.5117 2.87 0.3440 4.37 2.4 0.01253 0.00281
F∆ dn/dxF
?pT?∆?p2
T?∆
F∆ dn/dxF
?pT?∆?p2
T?∆
y
0.6715 1.17 0.8531 1.30 0.4157 0.65 0.2427 1.15 0.4762 1.04 0.6166 1.50 0.4002 0.68 0.2227 1.29 0.0 0.06635 0.04729
2.6 0.00754 0.00139
2.8 0.00353 0.00045
3.0 0.00113 0.00007
Table 5: pT integrated invariant cross section F [mb·c], density distribution dn/dxF, mean
transverse momentum ?pT? [GeV/c], mean transverse momentum squared ?p2
a function of xF, as well as density distribution dn/dy as a function of y for K+and K−. The
statistical uncertainty ∆ for each quantity is given in % as an upper limit considering the full
statistical error of each measured pT/xFbin
T? [(GeV/c)2] as
The statistical uncertainties of the integrated quantities given in Table 5 are upper lim
its obtained by using the full statistical fluctuations over the measured bins. As such they are
equivalent, for the kaon yields, to the statistical error of the total number of kaons contained in
each xFbin.
The resulting distributions are shown in Fig. 50 for K+and K−as a function of xFand
y. The relative statistical errors of all quantities are generally below the percent level. They
increase towards the high end of the available xF region essentially defined by the available
event number and, especially for K+, by limits concerning particle identification (Sect. 4). The
K+/K−ratio, ?pT? and ?p2
T? for kaons as a function of xFare presented in Fig. 51a–c. Fig. 51d
38
Page 41
shows the mean transverse momentum of all measured particle species in a single panel in
order to allow a general overview of the interesting evolution of this quantity with xF which
demonstrates that ?pT? is equal to within 0.05 GeV/c for all particles at xF∼ 0.3 – 0.4.
F
x
00.2 0.4
F
dn/dx
3
10
2
10
1
10
1
a)
+
K
K

F
x
00.2 0.4
c]
⋅
F [mb
2
10
1
10
1
b)
+
K
K

y
0123
dn/dy
4
10
3
10
2
10
1
10
1
c)
+
K
K

Figure 50: Integrated distributions of K+and K−produced in p+p interactions at 158 GeV/c:
a) density distribution dn/dxFas a function of xF; b) invariant cross section F as a function of
xF; c) density distribution dn/dy as a function of y
F
x
00.20.4

/K
+
K
0
2
4
6
a)
F
x
00.20.4
[GeV/c]
〉
p
〈
T
0
0.2
0.4
0.6
0.8
b)
+
K
K

F
x
00.20.4
]
2
[(GeV/c)
〉
2
p
〈
T
0
0.2
0.4
0.6
0.8
c)
F
x
0 0.2 0.4 0.6 0.8
[GeV/c]
〉
p
〈
T
0.2
0.3
0.4
0.5
0.6
d)
+
ππ
K
K
p
p
+
Figure 51: a) K+/K−ratio, b) mean pT, and c) mean p2
produced in p+p interactions at 158 GeV/c; d) mean pTfor π+, π−, K+, K−, p, p on an enlarged
vertical scale
Tas a function of xF for K+and K−
9.2Comparison to other data
As in Sect. 8, a first stage of the comparison is limited to the SPS/Fermilab energy range
where only two experiments provide integrated cross sections. The data of Brenner et al. [13]
are obtained from a limited set of double differential cross sections, using basically exponential
fits to the measured points. The resulting invariant cross sections F(xF) are shown in Fig. 52 in
comparison to the NA49 data.
As already remarked for the case of pions and protons, very sizeable deviations are
visiblein thedistributionsofFig. 52a, which arequantified bytheratioofthetwomeasurements
shown in Fig. 52b. If the relative differences in F were limited to about ±40% for pions and
protons [1,2], the factors are even bigger for kaons, with a mean deviation of about 50%. This
39
Page 42
F
x
00.20.4
c]
⋅
F [mb
3
10
2
10
1
10
1
a)
+
K
100 GeV
175 GeV

K
100 GeV
175 GeV
F
x
00.20.4
R
0
0.5
1
1.5
2
2.5
3
b)
+
K
〉
R
〈

K〉
R
〈
Figure 52: a) Comparison of pTintegrated invariant cross section F as a function of xFfor K+
and K−measured by [13] to NA49 results (represented as lines). The data for K−are multiplied
by 0.1; b) Ratio R between measurements of [13] and NA49 results. The mean ratios for K+
and K−are presented with dashed lines
again demonstrates the danger of using oversimplified algebraic parametrizations of double
differential data which comply with the NA49 measurements on the pointbypoint level within
their statistical errors (Sect. 8.1).
The EHS experiment [35] at the CERN SPS, using a 400 GeV/c proton beam, offers pT
integrated data which are directly comparable in all quantities defined in Eq. 15. In view of the
sdependence which is enhanced at low xFin the quantity dn/dxF[1,2] and of the important
shape change to be expected in the rapidity distributions, only the invariant integrated cross
section F is plotted in Fig. 53 in comparison to the NA49 data.
c]
⋅
F [mb
F
x
00.2 0.4
b)

K
F
x
0 0.20.4
0
0.2
0.4
0.6
0.8
1
a)
+
K
Figure 53: Comparison of pTintegrated invariant cross section F as a function of xFfor a) K+
and b) K−measured by [35] to NA49 results (represented as dashed lines)
Some remarks are in place here. The EHS K+data show an enhancement at low xFof
about 35% which is substantially above the expected sdependence, see also the discussion of
thekaon data in Sect. 13. After a local deviationfrom a smooth xFdependence at xF∼ 0.15 the
40
Page 43
distributioncuts, however, below theNA49 data in the region 0.175 < xF< 0.45. This decrease
cannot be explained by any known sdependence. For K−the situation is qualitatively similar.
Here at xF= 0 an enhancement of 41% is observed, with an xFdependence which smoothly
approaches the NA49 data to become equal to these cross sections within errors at xF > 0.22.
Again such behaviour contradicts the expected sdependence. A possible explanation might be
contained in the mean p2
the respective errors, the EHS data deviate rapidly upwards from the NA49 measurements with
increasing xF. For K+the instability in the cross sections at xF= 0.15 is seen as a break in the
xF dependence of ?p2
0.2 < xF< 0.45 which corresponds to the depletion of the cross section, rising again steeply to
very large values at xFbeyond the range accessible to NA49. A similar behaviour is observed
for K−where ?p2
the NA49 data which is however inconsistent with the sdependence in Sect. 10.6.4. Above
xF∼ 0.2, however, there is again a strong almost linear increase of ?p2
excess of 0.8 (GeV/c)2in the high xFregion. One may speculate that both the behaviour of the
invariant cross sections and the one of ?p2
detection losses for kaons with increasing xFand at transverse momenta below the mean value.
This would reduce the observed cross sections and enhance the mean p2
Tdata shown in Fig. 54. If the results on ?p2
T? agree at xF= 0 within
T? at the same xF value. The xF dependence then flattens in the region
T? shows reasonable consistency up to xF ∼ 0.2 with a slight increase over
T? with xFwith values in
T? are of the same origin if one assumes that there are
T.
]
2
[(GeV/c)
〉
2
p
〈
T
F
x
0 0.2 0.4
b)

K
F
x
0 0.20.4
0
0.2
0.4
0.6
0.8
1
a)
+
K
Figure 54: Comparison ?p2
results (represented as dashed lines)
T? as a function of xFfor a) K+and b) K−measured by [35] to NA49
In conclusion of the comparisons with the EHS experiment which have been carried out
with some precision for pions [1], baryons [2] and here for kaons, a somewhat unsatisfactory
and partially inconsistent picture emerges. In general it may be stated that sizeable relative
differences, evenafter taking intoaccount possiblesdependences, emerge at a leveloftypically
±10 – 30% which cannot be explained by a common factor like normalization uncertainties. In
addition there seems to be a general tendency of unphysical behaviour in the EHS data for xF
values above about 0.2 both in the cross sections and, more extremely, for the behaviour of
mean p2
T.
9.3Total kaon yields and mean charged multiplicity
For the xFintegration of the dn/dxFdistributions presented in Table 5 an exponential
extrapolation into the unmeasured region at high xFhas been used. This is well justified by the
shape of the distributions within the measured region and by the fact that only 4% (0.3%) of the
41
Page 44
total yields are beyond the experimental limits for K+and K−, respectively. The resulting total
kaon yields are:
?nK+? = 0.2267
?nK−? = 0.1303
?nK+?/?nK−? = 1.740
?nK+? + ?nK−?
2
= 0.1785
(16)
The statistical errors of these yields may be estimated by the total number of kaons
extracted from the 4.8M events of this experiment. These are 260k for K+and 170k for K−.
From these numbers follows, including the additional statistical errors from particle identifica
tion, Sect. 4.5 Fig. 12, an error of 0.27% for K+and 0.28% for K−which is about one order of
magnitude below the smallest estimated systematic error (Table 1).
These numbers, together with the results for pions [1] and baryons [2] can be used
to establish the mean charged multiplicity as it results from this experiment. The respective
numbers are given in Table 6 below.
positives
3.018
0.227
1.162
4.407
negatives
2.360
0.130
0.039
2.529
total
5.378
0.357
1.201
6.936
?nπ?
?nK?
?np?
?n?
Table 6: Mean multiplicities of charged particles
In orderto establishthetotal charged multiplicityand tobeable tocompareto theresults
from bubble chamber work where the charged hyperons are included as onvertex tracks, an
estimation of Σ+and Σ−yields has to be performed. Several measurements of Σ+, Σ−and
Σ0are available in the energy range 3 <√s < 27 GeV, all with rather big relative statistical
errors of typically 15 to 50%. For the present purpose where the charged hyperons constitute
a correction of about 1%, this is nevertheless acceptable since all results stem from bubble
chamber experiments with small systematic uncertainties. Three quantities are interesting and
necessary for the present comparison:
1. the Σ0/Λ ratio
2. the Σ+/Σ−ratio
3. the ratio (Σ−+ Σ0+ Σ+)/Λ
The Σ0/Λ ratio has been obtained by 5 experiments [36–40] with values between 0.1
and 0.74 with an average of 0.4. This value may be used to obtain the ratio (Σ−+ Σ0+ Σ+)/Λ
[41–43] which varies between 0.83 and 1.09 with an average of 0.99. The ratio Σ+/Σ−[39,41–
43,45]shows a variation from 2 to 5.2 with an average of 3.3.
Adopting the average values for the ratios (1) and (3) the combined yield Σ++ Σ−may
be obtained at√s = 17.2 GeV by interpolating the wellestablished total yield of Λ [39–44,46–
59] to ?nΛ? = 0.12 per inelastic event at this energy. This results in a contribution of 0.07 per
inelastic event from charged hyperons and gives a total charged multiplicity
?nch? = 7.01
(17)
42
Page 45
from this experiment. This multiplicity may be compared to the existing measurements essen
tially from Bubble Chamber experiments taken from [60] and presented in Fig. 55.
[GeV/c]
beam
p
0200400
ch
n
5
6
7
8
9
10
Figure 55: ?nch? as a function of beam momentum pbeam. The NA49 measurement is indicated
with an open circle
The full line in Fig. 55 represents a hand interpolation of the measurements in the range
from 50 to 300 GeV/c beam momentum. It coincides incidentally, at√s = 17.2 GeV, with the
parametrization
?nch? = −4.8 + 10/√s + 2.0lns
(18)
given by [61] which predicts
?nch? = 7.15
(19)
The relative deviation of the summed integrated yields given above from this value cor
responds to 2%. It is certainly governed by the systematic uncertainties of the dominant pion
and proton yields for which the systematic error estimation [1,2] gave 4.8% (5%) for the lin
ear sum and 2% (2.5%) for the more optimistic quadratic sum of the contributions,respectively.
Allowing for a typical error of about 1% of the bubble chamber data, it may be stated that the
observed deviation is within the error estimate for the NA49 data.
At this point it is indicated to also check the charge balance of the NA49 results where
the difference between positive and negative particle yields should give two units from charge
conservation. Using the total charged hyperon yield estimated above and the average Σ+/Σ−
ratio of 3.3 the following yields are obtained:
?nΣ+? = 0.054
?nΣ−? = 0.016
?npos? = 4.461
?nneg? = 2.545
?npos? − ?nneg? = 1.916
(20)
43
Page 46
This means that the charge balance is off by 0.08 units or about 4% of its nominal value.
In order to put this number into perspective it should be realized that a systematic downwards
deviation of the π+yield by 1.5% accompanied by an upward shift of the π−yield by the same
relative amount is sufficient to explain this imbalance. Therefore it may be stated that also the
charge conservation of the NA49 results is established within the stated systematic errors.
10A new evaluation of s dependence
The new set of kaon data presented and discussed above has been used, in connection
with existing data at other cms energies, to reassess the experimental situation as far as the
sdependence, in particular also for integrated yields, is concerned. It is indeed rather surprising
that the very first attempt in this direction by Rossi et al. [4] which dates from 1975, is still
being used as a reference for rather farreaching conclusions with respect to kaon production in
heavy ion interactions [62]. This is especially concerning the admitted systematic uncertainties
which are given in [4] as only 15% for their estimated total yields. In view of the rather sparse
phase space coverage of most of the preceding data sets, see Sect. 2 and Fig. 1 above, it is in fact
for most cms energies quite difficult to establish integrated yields with defendable reliability.
In this context it is interesting to also look at the available data on K0
ing for the srange up to medium ISR energies exclusively from bubble chamber experiments,
have well defined systematic errors in particular for integrated yields, notwithstanding their in
general rather limited statistical significance. Here, the relation between charged and neutral
kaon production deserves special attention as it is directly sensitive to the respective produc
tion mechanisms. In the following section, five energy ranges from Cosmotron up to RHIC and
collider energies will be inspected in an attempt at establishing some coherence with respect to
sdependence.
Sproduction which, com
10.1 The K+data of Hogan et al. [5] and Reed et al. [6] at√s = 2.9 GeV
These early experiments at the PrincetonPenn (PPA) and BNL Cosmotron accelerators
use a range of beam momenta from 3.2 to 3.9 GeV/c with a common point at about 3.7 GeV/c.
The data at this energy have been used in order to establish a maximum of combined phase
space coverage in the ranges 0 < xF < 0.4 and 0 < pT < 0.6 GeV/c, see Fig. 1a. It should
be mentioned here that the definition of xF(Eq. 2) has been used throughout although it pro
gressively limits the available xF range at low interaction energies due to energymomentum
conservation, see [8] for a detailed discussion. At√s = 3 GeV this means rather sharp cutoffs
in production cross section towards xF∼ 0.5 and pT∼ 0.7 GeV/c. Within these limits, reason
able inter or extraextrapolation may be performed in order to establish approximate pTand xF
dependences. It should be stressed that throughout this paper no arithmetic parametrizations of
xFor pTdistributions have been used as those would introduce large systematic biases which
are difficult to control. Instead, twodimensional interpolation by multistep eyeball fits, as dis
cussed in Sect. 6.2 above, have been applied. Two examples of this procedure are shown in
Fig. 56 for selected xFand pTvalues, where the available, interpolated or slightly extrapolated
data points are indicated. The resulting interpolation of cross sections over the complete xFand
pTranges is presented in Fig. 57.
The interpolation shown in Fig. 57 may be pT integrated in order to obtain the F,
dn/dxFand ?pT? dependences shown in Fig. 58.
In a second step the integration over xF may be performed resulting in an average
K+multiplicity of ?nK+? = 0.00481. This value is 8.3% (6.0%) higher than the multiplicities
?nK+? = 0.00441±17% and ?nK+? = 0.00452±23% obtained by [5] and [6], respectively. These
44
Page 47
)]
3
/c
2
f [mb/(GeV
[GeV/c]
T
p
00.20.40.60.8
b)
= 0.2
F
x
[GeV/c]
T
p
0 0.2 0.40.60.8
2
10
1
10
a)
= 0
F
x
[5]
[6]
Figure 56: f as a function of pTfor a) xF= 0 and b) xF= 0.2. The data points from Hogan et
al. [5] and Reed et al. [6] are given together with the data interpolation (full lines)
F
x
0 0.20.4 0.6
)]
3
/c
2
f [mb/(GeV
4
10
3
10
2
10
1
10
= 0.0 GeV/c
0.1
0.2
0.3
0.4
0.5
0.6
0.7
T
p
Figure 57: Interpolated invariant cross sections as a function of xFfor fixed values of pT
groups imposed isotropy (Swave decay) in the cms system in order to be able to carry out the
data integration. There is also a bubble chamber experiment from the BNL Cosmotron at the
same beam momentum [63] which gives ?nK+? = 0.00462±19% for the K+multiplicity which
is only 4% lower than the result obtained above. In conclusion a statisticallyconsistent K+yield
from 3 independent experiments may be claimed at√s = 3 GeV/c which is about 55% above
the one elaborated in [4].
The bubble chamber experiment [63] also gives the K0multiplicity as ?nK0? = 0.00165.
With the usual assumption ?nK0
S? = 0.5?nK0? this corresponds to ?nK0
S? = 0.000824. The ratio
RK0
SK± =0.5(?nK+? + ?nK−?)
?nK0
S?
(21)
45
Page 48
F
x
00.1 0.20.3 0.4
[GeV/c]
〉
p
〈
T
0
0.2
0.4
0.6
c)
F
x
0 0.1 0.20.30.4
F
dn/dx
3
10
2
10
1
10
1
b)
F
x
00.1 0.2 0.3 0.4
c]
⋅
F [mb
3
10
2
10
1
10
1
a)
[5,6]
NA49
Figure 58: pT integrated a) F, b) dn/dxF and c) ?pT? distributions as a function of xF. The
results obtained at√s = 17.2 GeV (dashed lines) are also shown for comparison
is therefore, with ?nK+? from [63] as given above, 2.8 which is substantially above the value
RK0
RK0
deviationfrom isospininvariancein kaon productionas thethreshold is approached from above,
as shown in Fig. 59.
SK± = 1 expected from isospin invariance. Inspecting the K0
SK± is determined to 1.4 at√s = 3.5 GeV and 1.27 at√s = 4 GeV. This indicates a steep
Sand K±data of [37] and [64],
[GeV]s
23456
±
K
0
K
S
R
1
2
3
Figure 59: Ratio RK0
The threshold of kaon production is indicated at about√s ∼ 2.5 GeV
SK± between the average charged kaon and K0
Syields as a function of√s.
Evidently RK0
SK± = 1 may be assumed within a few percent error margin at√s > 5 GeV, see Sect. 11
below for a more detailed discussion.
It is also interesting to compare the differential data of [5] and [6] directly to the NA49
data. The ratio of the invariant inclusive cross sections,
SK± approaches unity rather quickly with increasing energy so that
RK0
Rs=
f(xF,pT,√s = 3 GeV)
f(xF,pT,√s = 17.2 GeV)
(22)
is shown in Fig. 60 as a function of pTat constant xFand as a function of xFat constant values
of pT.
46
Page 49
s
R
F
x
00.20.40.6
= 0.0 GeV/c
= 0.2 GeV/c
= 0.4 GeV/c
T
p
p
p
T
T
b)
[GeV/c]
T
p
00.2 0.40.60.8
0
0.05
0.1
0.15
0.2
0.0
0.1
0.2
= 0.3
F
x
0.4
a)
Figure 60: Ratio Rsas a function of a) pTat fixed xFand b) xFat fixed pT
Evidently the total yield ratio of 0.021 does not translate into a common suppression
factor for the differential distributions but the local cross section ratios show a strong and com
plex dependence on the kinematical variables. If the complete suppression of K+production for
pT? 0.7 GeV/c and xF? 0.5 is a trivial consequence of energymomentum conservation, the
local structures as for instance the maximum at xF∼ 0.3 and low pTare a consequence of the
evolution of different production mechanisms with increasing interaction energy.
10.2Data in the PS/AGS energy range
In this subsection data in a range from 12.5 to 24 GeV/c beam momentum are grouped
together, again in an effort to consolidate the available information and to quantify the consis
tency of the different data sets. This concerns the double differential data by Akerlof et al. [9] at
12.5 GeV/c beam momentum, of Dekkers et al. [10] at 18.8 and 23.1 GeV/c, and the extensive
data sets of the CERN/Rome group, Allaby et al. [7,8] at 14.2, 19.2 and 24 GeV/c beam mo
mentum. The data sets from all these groups have been tabulated conveniently by Diddens and
Schl¨ upmann in Landoldt B¨ ornstein [65]. As the overview of Fig. 1b shows, there is a fair cov
erage of phase space and some mutual overlap, unfortunately again [1,2] with the exception of
the low xFregion, xF< 0.1–0.15, at all pT. In a first step, the Allaby et al. data [7,8] are trans
formed to the standard xFvalues following Eq. 2 and interpolated using the twodimensional,
multistep eyeball method described in sect. 6.2. An extrapolation into the nonmeasured phase
space areas is then attempted in order to allow the establishment of integrated yields. The situ
ation may be judged from Fig. 61 where the interpolated/extrapolated cross sections are shown
as a function of xFat fixed values of pTfor K+, Fig. 61a, and K−, Fig. 61b. Here the regions
with available measurements from [7,8] are marked by the hatched areas.
Clearly, the above remark concerning the problems with data extrapolation is well in
place here, especially for the higher pTregions. However, at least towards low pTthere is not
much freedom of choice, as well as for the pTregion 0 < pT < 1 GeV/c towards xF= 0. Up
to pT ∼ 1 GeV/c it is hard to imagine an extrapolation which would be off by more than, say,
1020% from the lines shown at xF= 0. It is also clear that the increasing error margin towards
higher pTwill not contribute too much to the integrated cross sections. The ratio
47
Page 50
)]
3
/c
2
f [mb/(GeV
F
x
00.20.40.60.8
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
[GeV/c]
T
p

K
F
x
0 0.20.40.60.8
7
10
6
10
5
10
4
10
3
10
2
10
1
10
1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
[GeV/c]
T
p
+
K
Figure 61: Invariant, inter/extrapolated cross sections as a function of xFfor fixed values of pT
for a) K+and b) K−. The xF, pTregions covered by data are indicated as the hatched areas
Rs=
f(xF,pT,√s = 6.8 GeV)
f(xF,pT,√s = 17.2 GeV)
(23)
is shown in Fig. 62 for K−and K+as a function of pTand xF.
s
R
s
R
[GeV/c]
T
p
F
x
b)

K
= 0.0 GeV/c
T
0.2
0.4
0.6
0.8
1.0
1.2
1.4
p
0
0.5
1
a)

K
0.0
0.05
0.1
0.15
0.2
= 0.3
F
x
0.4
00.20.4
= 0.2 GeV/c
T
p
0.6
0.8
1.0
1.2
1.4
d)
+
K
00.51 1.5
0
0.5
1
= 0.0
F
x
0.1
0.15
0.2
0.3
0.4
c)
+
K
Figure 62: Rsa) as a function of pTat fixed xFand b) as a function of xFfor fixed pTfor K−
and c) as a function of pTat fixed xFand d) as a function of xFfor fixed pTfor K+
48
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