Scalar and vector meson production and two-step processes in the (K−, K+) reaction on 12C

NUCLEAR PHYSICS ELSEVlER

Nuclear Physics

A

A 625 ( 1997) 231-250

Scalar and vector meson production and two-step processes in the (K-, K+) reaction on 12C E224 Collaboration J.K. Ahn”, S. Aokid, K.S. Chungk, M.S. Chungj, H. En’yo”, T. Fukudae, H. Funahashi a, Y. Goto a,*, A. Higashi e, M. Ieiri f, T. Iijima f, M. Iinuma a, K. Imai a, Y. Itow a,2, J.M. Lee k, S. Makino ‘, A. Masaike a, Y. Matsuda a, Y. Matsuyama e, S. Miharaa, C. Nagoshi e, I. Nomurah, I.S. Parkj, N. Saito”-‘, M. Sekimotoe, Y.M. Shin’, K .S . Simj, R. Susukita”,‘, R. Takashima b, F. TakeutchiC, P. Tlusty e,3, S. Weibe i, S. Yokkaichi a, K. Yoshida”, M. Yoshidaa,‘, T. Yoshidas, S. Yamashita a ’ Department of Physics, Kyoto University Kitashirakawa-Oiwake, Kyoto 606, Japan h Kyoto Umversity of Education, Fukakusa-Fujinomori, Kyoto 612, Japan ’ Kyoto Sangyo University Kamigamo-Motoyama, Kyoto 606, Japan d Faculty of Human Development, Kobe University, Nada, Kobe 657, Japan ’ Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188, Japan f KEK, National Laboratory for High Energy Physics, Oho, Tsukuba 305, Japan g Department of Physics, Osaka City University Sumiyoshi, Osaka 558, Japan h National Institute for Fusion Science, Nagoya 464-01, Japan i University of Saskatchewan, Saskatoon. Canada i Department of Physics, Korea University, Seoul 136-701, South Koreu k Department of Physics, Yonsei University. Seoul 120-749, South Koreu Received 7 January

1997; revised 14 May 1997

Abstract The double strangeness exchange reaction (K-, K’) is investigated with respect to the subthreshold production of scalar and vector mesons (Jr/ao/~$) decaying into K+ K- and the twostep processes induced by intermediate mesons and a- hyperons at pk- = 1.66 GeV/c using a scintillating fiber active target. The differential cross section ((dg/d&)) averaged over the angular interval (2.3” < Sk+ < 14.7’) for the sub-threshold fa/aa/q!~ meson production with the KfKdecay is 1 I f 6 pb/sr at 0.6 < p k+ < 0.95 GeV/c. The present result differs significantly from the theoretical calculation which predicts the contribution of the fa/ao/#r meson production to be predominant in the (K- , K+ ) reaction below pk~ = 0.95 GeVlc. We found a sizable contribution from two-step (K-, K+) processes, characterized by production of two S = ~ 1 037%9474/97/$17.00 @ 1997 Published PIISO375-9474(96)00319-9

by Elsevier Science B.V. All rights reserved.

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E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

hyperons, consistent with the result of the intra-nuclear cascade (INC) model calculation with respect to the meson-induced hyperon (or hyperon resonance) pair production in the momentum region 0.6 ~< P m < 0.95 GeV/c. The observed enhancement of the cross section for the two-step AA production beyond the prediction of the INC model at Pm '~ 1.1 GeV/c could be due to the ~,~-p --+ A A reaction in 12C. @ 1997 Published by Elsevier Science B.V. PACS: 25.80.Nv Keywords: (K°, K+ ) reaction at PK- = 1.66 GeV/c; Subthreshold fo/ao/fb meson production; Two-step

process; Quasi-free ~ * - production

1. Introduction The ( K - , K +) reaction on nuclei has attracted much attention since it was predicted to be an efficient channel for production of both H dibaryon and double strangeness nuclei, such as ~ and A A hypernuclei [ 1-3 ]. Several experiments have been carried out to search for the H dibaryon and double strangeness nuclei produced through ( K - , K + ) reactions at incident K - momenta from 1.65 to 1.8 G e V / c [ 4 - 8 ] . The H dibaryon was sought using ( K - , K +) reactions on 3He (BNL-E836) [4], nuclear emulsion (KEK-E176) [5], and scintillating fiber active target (KEK-E224) [6]. Evidence of the H dibaryon has, to this point, not been observed in these experiments. On the other hand, experiments demonstrating the production of double A hypernuclei as a result of the ( K - , K +) reaction on emulsion nuclei and as a result of the stopping of ~ - in the emulsion have been reported [9,10]. In order to extend such studies, it is quite important to understand the mechanism of the ( K - , K +) reaction on nuclei. The ( K - , K +) reaction is itself of considerable intrinsic interest in the field of nuclear reactions since it is a double-charge and double-strangeness exchange reaction. Elementary reactions such as K - p --~ K + ~ - and K - p --~ K + ~ * - were studied quite some time ago in a number of experiments employing hydrogen bubble chambers [ 11 ]. The ( K - , K +) reaction on nuclei was also observed in a heavy liquid bubble chamber at PK- = 2.1 G e V / c [ 12]. However, the statistics in these experiments were too limited for the investigation of the reaction mechanism, and emphasis was laid on the resonance search in the A A and ~ - p invariant mass spectra. Recently, Iijima et al. measured cross sections for the ( K - , K +) reaction on nuclear targets of C, AI, Cu, Ag and Pb at PK = 1.65 G e V / c [13]. For all these nuclear targets, K + momentum spectra were characterized by a peak at P m ~- 1.1 G e V / c and a large bump centered around pK, -~ 0.6 G e V / c , corresponding kinematically to quasi-free ~ - and ~ * - production, respectively. The cross section for the upper peak was reproduced well by the D W I A Present address: RIKEN, Institute for Physical and Chemical Research, Wako, 351-01, Japan. 2 Present address: Institute for Cosmic Ray Research, University of Tokyo, Tanashi, Tokyo 188, Japan. 3 Present address: Nuclear Physics Institute of the Academy of Science, 250 68 P,e~, (~zech Republic. 4 Present address: International Center for Elementary Particle Physics, University of Tokyo, Tokyo 113, Japan.

E22.4 Collaboration~Nuclear

Physics A 625 (1997) 231-250

233

Table 1 Threshold momenta for K---induced reactions Reaction

Threshold K - laboratory momentum

K - + p ~ K+ + ~ K - + p ~ K+ + ~ * K - + p ~ .fi~/ao/fa + A

1.05 (G e V / c ) 1.52 1.70/1.72/1.76

calculation for the quasi-free K - p ~ K + ~ - process. However, the cross section for the lower bump was measured to be a factor of 4 ~ 6 times larger than that predicted by the DWIA calculation for the quasi-free K - p - ~ K + ~ * - reaction [ 13]. This raised an intriguing question. Iijima et al. proposed that the large value measured for the cross section could be due largely to intermediate meson-induced two-step processes such as K - N -+ trY, 7rN --+ K + Y , where Y denotes A or 27 [ 13]. However, recently Gobbi et al. interpreted the low momentum bump in the ( K - , K +) reaction as being due to first order K - p ~ f o (975) A, a0(980) A and q~(1020) A reactions, followed in part by the decay f o / a o / O 5 --~ K - K + [14]. The meson-induced two-step ( K - , K +) reactions, they predicted, would occur' on nuclei only at the level of 1% of the first order processes at 1.65 GeV/c. More recently, Nara et al. reproduced the K + momentum spectra for ( K - , K + ) reactions on nuclear targets at P x - = 1.65 GeV/c using an intra-nuclear cascade (INC) model calculation [15]. The INC model calculation for the first order processes is consistent with the relativistic impulse approximation (RIA) calculation, while the INC result for the scalar and vector meson production is roughly a factor of two smaller than the result of Gobbi et al. [ 14,15]. On the other hand, the INC model calculation for the two-step processes suggests that sizable contributions must arise from the mesoninduced two-step strangeness exchange reactions with all possible meson and hyperon families. It should be noted that scalar and vector mesons are produced at sub-threshold energy, as shown in Table 1, and the nucleon momentum distribution plays a crucial role in the evaluation of the cross sections. The approximate treatment of Gobbi et al. for the effect of Fermi motion yields an inconsistent result with the INC calculation. Moreover, there is no experimental result for the K - p --~ cbA reaction available between the threshold momentum (1.76 GeV/c) and 1.95 GeV/c, and the K - p --+ f o A / a o A reactions and the branching ratio of a0(980) --~ K - K + are not yet known precisely. We have carried out an experiment to observe the ( K - , K + ) reaction on a scintillating fiber (SCIFI) active target using a 1.66 GeV/c K - beam. The primary motivation of the experiment was to search for the H dibaryon through the direct process, K - ( p p ) - ~ H K + [ 16], and atomic capture process, (,--,~,C)atom ---+ H X [ 6 ] . At the same time, the details of the ( K - , K ~) reaction on 12C can be studied using the visual information obtained from the SCIFI target. The SCIFI target acts as both an interaction target and track detector, and provides an image of charged particle tracks around the ( K - , K ~) reaction vertex. It has an advantage over a bubble chamber with respect to the attainable

E224 Collaboration/NuclearPhysics A 625 (1997) 231-250

234

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'tt~

~ 3 "/~

/

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Fig. 1. Experimental setup. (A) Beam line elements and detectors upstream of the target. (B) SCIFI target and K+ tagging spectrometer. statistics due to its speed and triggerability, and the data can be easily analyzed by a computer. The target composition is simple (CH) in comparison with an emulsion, and the A production can be easily identified. This is essential in studying the reaction channels with A production. In this paper, we describe the results of the SCIFI data analysis from 2148 events in a fiducial volume, in order to study the ( K - , K +) reaction mechanism in a wide range of the K ÷ particle momentum. We report the cross section for the fo/ao/fb meson production at sub-threshold energy, as well as those for the two-step processes with respect to the final hyperon states, the 12C(K-, K+)AAX, 12C(K-, K + ) A X - X , and J 2 C ( K - , K + ) X + X - X reactions at PK- = 1.66 GeV/c. In addition, the production of ~ * - from lZc is discussed.

2. E x p e r i m e n t The experiment was carried out using a separated K - beam at the KEK proton synchrotron. The experimental setup is depicted in Fig. 1. The K - / ¢ r - ratio of the beam was typically 1/4 at an intensity of 2 x 104K - / s p i l l (--,2 s). The central momentum of the K - beam was 1.66 G e V / c with a spread of 0.06 G e V / c ( F W H M ) . The incident K - were identified with an aerogel Cherenkov detector (BAC). Together with the timeof-flight (TOF) information (T2-T1, At = 85 ps [ r m s ] ) , the contamination o f 7"rand/5 was reduced to less than 0.01%. The beam momentum was measured using eight planes of multi-wire proportional chambers (BPC1-5) with a resolution of A p / p = 0.5% (rms) [18].

235

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250 i t

SCIFI sheet~ X Y ~,

read out -

~

/

>-

o-4 ! 0

IIT-X

X view Fig. 2. Schematic view of the SCIFI target.

The momenta of outgoing particles were measured by a K + spectrometer consisting of a dipole magnet with a field integral of 1.08 T m, four drift chamber planes (DC1) at the entrance of the magnet, and eight drift chamber planes (DC2 and DC3) at the exit of the magnet. The momentum resolution (AP/P) was 0.5% (rms) at 1.2 GeV/c [6]. A hodoscope (CH) consisting of twelve plastic scintillators was placed before the magnet, and a TOF hodoscope (FTOF) consisting of 24 plastic scintillators was located 5 m downstream from the SCIFI target. The TOF was measured with the FTOF hodoscope and the T2 scintillation counter, and the overall time resolution of the TOF measurement was 110 ps (rms). The vertical hodoscope (YH) with six plastic scintillators defined the geometrical acceptance of the spectrometer, which was about 0.09 sr. The lucite (LC) and aerogel Cherenkov (SAC) detectors discriminated kaons from protons and 7r's. The refractive indices for the LC and the SAC were 1.59 and 1.04, respectively. The SCIFI target was made of scintillating fibers of a 0.5 mm square shape. It contained almost equal numbers of carbon and hydrogen atoms. As shown in Fig. 2, 200 flat sheets, each consisting of 160 plastic fibers, were stacked to form a 8 × 8 × 10 cm 3 block. The fiber sheets were laid alternately in X and Y directions, i.e. transverse to the beam, aligned along tile Z direction. The SCIFI target was viewed using two sets of the image intensifier tubes (IIT), which were arranged orthogonally along the X and Y directions. The spacing between adjacent fiber sheets out of the target volume was tapered to match the 8x 10 cm 2 target area (XZ and Y-Z) of each direction to the effective photo-sensitive area (8 cm Q) of the IIT. Black acryl plates of 300/zm thickness were inserted between the fiber sheets out of the target volume to prevent crosstalks. The IIT (Delft PP0040) possesses a cascade structure of three individual IIT's. The second and third stage IIT's are triggerable. The intensified image was viewed with a CCD camera and digitized by a flash ADC. The response of the SCIFI target to the charged

236

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

particles passing through its effective volume was to produce an array of spots along the particle tracks on the CCD image. A spot consists of a contiguous two-dimensional cluster of above-threshold pixels on the CCD. The average number of clusters for a minimum ionizing particle was about 0.55/mm along the track for each direction, and the size of a single cluster was typically 180/zm (rms). The track residual, defined as the distribution of the distance between the fitted straight track and each cluster, weighted by the brightness of each cluster, was about 2 9 0 / z m [ 19]. The SCIFI target was surrounded by a cylindrical drift chamber (CDC) and by TOF counters (BTOF) to detect particles coming out of the SCIFI target. The details of this detector will be reported elsewhere [20]. Due to the read-out frequency of the CCD (30 Hz), a fast and efficient method was needed to reduce the trigger rate to a manageable level, about 20 events/spill. To accomplish this, the trigger system was divided into two stages. The first level trigger selected positively charged particles passing through the YH, which were discriminated from zr's and protons by Cherenkov counters (SAC and LC). The coincidence of hit information between the FTOF and the CH enabled us to determine the electric charge of outgoing particles within the 2.4 /zs time interval characterizing the decay of the phosphor of the first stage IIT's. The second level trigger was made with fast electronics to calculate the masses of the scattered particles within a time of 15 /zs, using TOF information obtained with a fast encoding TDC system (LeCroy TAC + FERA ADC) and momenta determined by hit positions on the FTOF and the CH. The first level trigger signal gated the second stage liT's, while the second level trigger signal was applied to the last stage IIT's. The low momentum K ÷ were largely suppressed by the second level trigger, since the K + spectrometer and trigger system were designed to tag the high momentum K + which were accompanied by low energy ~ - . This suppression resulted in triggering approximately two thirds of 700 M e V / c particles and one fifth of 600 M e V / c particles, while high momentum particles (over 800 MeV/c) were most readily accepted. The trigger efficiency for scattered K ÷, determined largely by the second level trigger, was given by the ratio of the number of triggered K + particles at the first level trigger to the number of triggered K + particles at the second level trigger. This value was found to range from approximately 0.30 to 0.95 in the momentum region 600 ~< p x , <~ 1300 MeV/c. The total dead-time during the online data-taking was 20%.

3. Data analysis The tagged K + particles were selectively discriminated from zr+'s and protons by off-line analysis. The K + momentum and the missing mass spectra are shown in Fig. 3. A proton target was assumed for the calculation of the missing mass. Both spectra were obtained by selecting K + particles whose reconstructed mass ranges from 440 M e V / c 2 to 550 M e V / c 2. The background ratio of 7r+ and proton to K + was estimated to be less than 2%, assuming long-tail distributions for the ~-+ and proton are such that the constant background is below the K ÷ peak in the mass distribution.

,{tttt

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250 u

120

~ 100 m

g 8o "6 60

237

E = 4-0

7

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400

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600

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700

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800

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900

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1000 1100 1200 1300 t400 K+ Momentum (MeV/c)

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1400

i

i

i

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1450

i

i

t

i

i

L

i

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1500 1550 1600 Missinq Mass (MeV/c 2)

Fig. 3. K + momentum spectrum (top) and missing mass spectrum (bottom). A proton target was assumed to calculate missing mass.

A total of 3147 events were eye-scanned to investigate the mechanisms of the ( K - , K +) reactions. The scanning volume was geometrically limited to the effective target volume viewed by the IIT-CCD read-out system. The fiducial volume for the interaction point (Zvtx) along the beam direction was more tightly defined to result in a reliable event selection. This volume covered the region defined by - 5 0 mm ~< Zvtx ~< +36 mrn at the center of the SCIFI target. Out of the 3147 events, 2148 events were identified as interaction events within the fiducial volume. The number of events at high K + momenta (PK, ~> 950 MeV/c) was 1355, while that at low K + momenta was 793. We categorized all the 2148 interaction events with respect to their event topologies, defined by the numbers of charged prongs, kinks and A particles. They were globally divided into five groups, referred to as D, Y, I, K and X-types. Schematic drawings of the event topologies are given in Fig. 4. The D-type and Y-type events have subsets of the DV-type and YV-type, respectively, characterized by visible A decay. The DV-type is defined as the event topology in which a 2 - particle (or other particles) decays into A and ~ - , and the A decays visibly. In the case that the A originated from a kink point, the DV-type event was studied further for the 2 * - 4 ~ - ~ . 0 channel at low K + momenta. The D-type is the parent

238

E224 Collaboration/Nuclear Physics A 625 (1997) 231-250 K+ \

i

Kq- ~,

K+ ~,

K(a) D(DV)-type (b)Y(YV)-type

K-I

(c) l-type

K-

(d) K-type

(e) X-type

Fig. 4. Event topologies of (K-, K+ ) reaction. Table 2 Event topology of (K-, K+ ) reactions Topology

D (DV)

Y (YV)

1

K

X

Total

# of events (all) # of events (PK~ ~< 950 MeV/c)

787 (281) 154 (35)

479 (97) 241 (62)

316 89

293 100

273 199

2148 793

set of the DV-type, and it also contains the events in which A decay is missing (A escapes or decays into neutrals). The Y-type and YV-type are defined in a similar manner. The Y-type has only one additional prong, which is consistent with the 7r+ or K - track, while the YV-type is the Y-type with a visible A decay. The I-type event is the interaction of the ~ - particle. In this case one charged prong comes out of the primary vertex and stops within the scanning volume. This prong, however, contains the stopping protons, which probably come from the nuclear evaporation of 12C, as well as the stopping ~ - K-type events have no additional prongs at the vertex. The immediate nuclear absorption o f = ' - particles and the subsequent emission of neutral particles are plausible processes in K-type events. Finally, the X-type includes all the multi-prong (more than two prongs distinct from the K + track) events, which are due largely to the multi-step process inside carbon nuclei. Computerized eye-scanning allowed for a minimization of human error in topology recognition. The ( K - , K +) event selection was carried out with the aid of the chamber data. The chamber data were graphically guided to filter ghost tracks which were not associated with the ( K - , K +) reaction. Moreover, comparison between two projection views (in the X Z and YZ planes) enabled us to determine most reliably the interaction, decay and stopping vertices. Approximately one tenth of total data were doubly eyescanned independently. The error associated with the human-dependent categorization was less than 6%, and the difference in the position measurements for the K - interaction vertex was 1 mm (rms) in the beam direction ( Z ) . A number of the = ' - and A decays were investigated to estimate the detection efficiency for the eye-scanning, found to be almost 100% if the decay length was longer than 5 mm [ 19]. Corrections due to uncertainties in identifying small angle and short decays were addressed by scanning efficiencies for each specific reaction. Since further selection criteria are imposed on reconstructing the specific reactions, it is possible to obtain an event sample which is almost free from uncertainties due to categorization with respect to event topology. The results of the categorization are shown in Table 2.

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239

3.1. Y-type

Possible processes belonging to the Y-type are the K - p ~ f o A , aoA, and ~bA reactions, followed by the fo/ao/qb --* K - K + decay, and the quasi-free K - p --~ K+ ~ *reaction with the ~ * - ~ -='°Tr- decay. The decay product, K - or 7r-, corresponds to the additional prong, which characterizes Y-type events. Most of the other ~ * - --~ E - T r ° decay events possess topologies resembling that of the D-type, while a small portion of these events involving a short ~ - hyperon may fall into the Y-type. If the f o / a o / ( ~ meson productions are predominant, as predicted by Gobbi et al., their K - K + decay topologies should be observed in Y-type events, despite the narrow experimental acceptance, which falls to zero below px+ = 500 MeV/c. The following selection criteria have been applied to select the K - p --+ f o A , aoA and ~A reactions, followed by f o / a o / f b --+ K - K + decays. ( l ) Events were required to exhibit a visible A decay due to which a decay proton should be stopped inside the scanning volume. (2) The missing mass should be larger than 1450 M e V / c 2 to effectively eliminate contributions from other processes. (3) The opening angle between K + and the other charged prong at the primary vertex should be less than 30 ° . (4) The reconstructed A mass with the primary vertex should be located within the tolerance window of I m A -- 1115.7 (MeV/c2)[ ~< 60 ( M e V / c 2 ) / L A , where LA is the flight length of A in mm, and 60 M e V / c 2 is the mass tolerance arising from the systematic error due to the angular resolution, 30 = 5 0 0 / R p (mrad), which depends on the range of the stopping proton (Rp in mm). The background contribution due to the ~0 and the short ~ - can be suppressed by requiring a visible A decay. Since the average flight length of the ~0 hyperon is 3.5 cm ( c r ~ ~- 8.71 cm) in the SCIFI target, the probability of visible A decay (crA ~- 7.89 cm) from the ~ becomes small. Moreover, the background contribution due to the ~ and the short ~ - is more significantly suppressed by the additional criterion on the A decay that the decay proton stops within the scanning volume. This is because the A momentum in the f o / a o / c k production is rather a good deal larger than that for the background. In addition, the flight length of a A particle accompanied by fo/ao/qb production is potentially longer than that for the background, since the origin of the A particle is different in two cases. The A masses were reconstructed from the decay angles of the proton and 7r- and the range of the proton. The kinetic energy of the stopping proton was deduced from an empirical lbrmula (inferred from the experimental data [ 19]). To insure that none of e+e - pairs were misidentified for A particle, we excluded events whose tracks were curled in the scanning volume. The curled tracks are attributed to e - e + pair production from low energy gamma rays under a fringe field of about 30 Gs. Energetic e÷e - pairs should escape from the scanning volume. Such pairs could originate from rr ° decay. Since we selected A which decayed into p and rr- with the proton stopping inside the scanning volume, energetic e - e + pairs of this nature were excluded.

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E224 Collaboration/Nuclear Physics A 625 (1997) 231-250

Fig. 5. Typicalevent of scalar and vector meson production. The K- K+ pair and A decay are clearly seen in both XZ and YZ directions (Z is the beam direction). The rationale behind the opening angle selection is that the OZI allowed decay ~b ~ K K has very little phase-space available since the ~b mass (1020 M e V / c 2) is barely above the K K threshold. Hence, the K + K - pair are Lorentz-boosted toward forward angles. Monte Carlo studies indicate that opening angles for the K - K + pairs lie below 30 °. After imposing these selection criteria, six events remained at 600 ~< px~ < 950 MeV/c. A typical SCIFI image of the fo/ao/~b meson production is shown in Fig. 5. 3.2. D-type

D-type events are largely populated in the ~ - production region, while they are uniformly distributed at low K + momenta. Below the ~ - production peak, D-type events display two first order processes. One of these is the K - " p " ~ ~ - K + reaction off a bound proton inside 12C, and the other is the K - p --* ~ * - K + reaction, followed by ~ * - ~ -~-Tr °. There is also a contribution from two-step processes, such as K - p --~ 7r+S-; rr+n ~ K+A. To resolve the contribution from the quasi-free K - p --~ ~ * - K + reaction, followed by -~*- ~ ~ - ~ 0 , all DV-type events at low K + momenta were investigated with selection criteria similar to those stipulated in fo/ao/qb production events (conditions ( 1 ) and ( 4 ) ) . Here instead of the opening angle criterion (condition ( 3 ) ) , a coplanar condition on the ~ - ~ ATr- decay plane was imposed to reconstruct the - ~ - . The coplanarity angle, ~, is defined as ~b = 90 ° - c o s - l ( k = - x k ~ - • k A ) , and must be less than 30 °. In addition, we require the reconstructed ~ - momenta to be larger than 300 MeV/c. Out of 35 DV-type events, 14 events were identified as DV-type (stopping p ) , for which the A decayed into p and 7r-, and this decay proton was stopped in the scanning volume. After imposing the above selection criteria, seven events remained as candidate events for the process K - p --~ ~ * - K + followed by ~ * - --* ~ - T r °. The other seven events gave results favoring the 12C(K-, K ÷) A 2 - X reaction hypothesis, for which the

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

241

Fig. 6. Typical AA production event. Two A decays are clearly seen in the bottom of the figure. data agree with A and X - production at the K - interaction vertex. The events were selected by requiring the A mass to match with the K - interaction point, within the tolerance window described in Section 3.1, and to not match with the kink point of the other charged particle. The kink tracks were identified for a charged baryon decaying into a meson and neutral(s). The assignment of the decaying (kinked) particle is allowed only for an S = - 1 charged hyperon decaying into a charged meson and neutral(s). In this case the particle is X-. 3.3. T w o A e v e n t s

Analysis of events having two A particles plays a major role in determining the kind of process which causes the lower bump at low K + momenta. The two A particles can be produced via the following two-step processes:

K-N---~

;

N--* K +

,

\, .~* J K-p

--+ K + ~ - ;

~-p

---+ A A , ~ ° A .

The two A events are further categorized in Table 3, with respect to the number of additional charged prongs at the primary vertices. The minimum length and opening angle requirements of decay particles were imposed to make a reliable selection of the A. Both decay particles were required to leave tracks of length greater than 2 mm, and the opening angle was required to be larger than 360, where ~0 is 500 m r a d / L mm, and L is the flight length of the decay particle. A typical A A production event is shown in Fig. 6. The fact that there exists no additional prong indicates that both A particles came from the two-step processes accompanied by A or ~,0 production in the first and sec-

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Table 3 Number of charged prongs in two A events # of prongs (event topology)

0(K)

l-stop (I)

l-escape (Y)

/> 2(X)

Total

# of events (all) # of events (PK+ < 950 MeV/c)

14 7

11 7

2 2

1 1

28 17

ond processes. Two events containing one escaping track can be understood as a ,Y* production followed by ATr+ decay. The remaining events possess one or more charged baryons, and are most likely due to nuclear evaporation of residual nuclei during the two-step process.

4. Results and discussion The production cross section was evaluated by using the absolute cross section data of the experiment of Iijima et al. [ 13]. The angular distribution for the K - p --~ K + ~ reaction was inferred from data taken from a hydrogen bubble chamber experiment [ 11 ]. The differential cross section averaged over an angular interval is given by COSOm~ a a l l

=

/

7-A--d( cos 0)

i '

COS 0rain

L

COSimax

d(cos0),

/

(1)

COS0rain

where 0man = 2.3 ° and 0max = 14.7 °. The differential cross section averaged over the above angular interval

K - , , p " ~ K + .U-

was deduced from the product of the effective proton number of the SCIFI target and the differential cross section averaged over the angular acceptance, d g ~ L / x p--,K+~- x (1 + Z e ~ ) = 1 1 6 + 13 # b / s r , where Ze~ = 2.36 [ 13,22]. The differential cross section averaged over the angular interval is given by

do- \SCIH

75;/

V = NOrlsFOrl(pK+,Om)si,~TK+dec,

(2)

where Y is the experimental yield, and ~ s ~ is the detection efficiency with the SCIFI target. The function ~/(Pm, OK+)St' represents the experimental acceptance of the spectrometer, and "r]K+dec accounts for the survival rate of the scattered K + particle traveling

E224 Collaboration/Nuclear Physics A 625 (1997) 231-250

243

up to the FTOF counter, placed 5 m away from the target center. No is the normalization factor, which is given by do- ~SCIF1 No =

d~L/K

, ( p K + ,OK+ ) s ; " T]K2-dec

"P"~K+~- N(P~>950 MeV/c) n t (p~>950MeV/c) " (K_,K~) • l~E - / 9 ~

(3)

N(P~>950MeV/c)

Here, (K-,K+) is the experimental yield of the ( K - , K +) reaction above PK~ = 950 M e V / c with the SCIFI target. The ratio of the number of E - produced to the number of ( K - , K +) reactions, R = - , was 0.81 :k 0.033 at high K + momenta (950 M e V / c <~ PK, <. 1300 M e V / c ) [23]. The factor gl(p/>950 MeV/c) represents the probability that =-_ the K + momenta in the K - p --+ K + E - reactions lie above 950 MeV/c. This value was estimated to be 0.90. A Monte Carlo simulation was performed to estimate the online detection efficiency of K + particles as a function of the K + momentum and the efficiency of the SCIFI target. The Monte Carlo simulation reproduced the momentum dependence of the experimental acceptance for K + particles with a 5% error on average in the region 600 ~< PK, < 800 M e V / c ( ~ 1 % error for 800 ~< PK, <. 1300 MeV/c). In the target region, all systematic factors scaling down the detection efficiency were included in the procedure of the Monte Carlo simulation. To demonstrate the reliability of the simulation, the response function of the SCIFI detector was examined for the reaction K - p -+ K+,~ followed by _~- --+ Arr-. The ratio of the number of visible A decays to the total number of quasi-free E - produced was sensitive to both the geometry of the SCIFI target and the scanning efficiency. The Monte Carlo simulation produced the result that 38% of the A decayed visibly inside the scanning volume. This value is consistent with that obtained experimentally, 39 4- 3%. 4.1. Scalar and vector meson production

Despite detection of all the charged final states, the masses of the f o / a o / 4 ) mesons could not be kinematically reconstructed, since they were all produced off the bound protons moving inside 12C. A great deal of attention was paid to the estimation of the detection efficiency and background in order to obtain the cross section for scalar and vector meson production. The differential cross section for f o / a o / 4 ) meson production was calculated as

( do- ~ SC1FI

YA(st°ppingp)M(--+K-K+)

(4)

/ A(g ~ K- K+) = NO r/SFD " r/( PK +, OK+ ) SP" rB¢~dec' where M denotes the f0, a0 and ~b mesons. The experimental yield, YA(stoppingp)M(---~K-K~), is the number of events for which the A particle decays visibly with its decay proton stopping within the scanning volume with f o / a o / f b mesons decaying into K - K +. The quantity r/sw accounts for the scanning efficiency of finding a visible A decay with a stopping proton, and its value was estimated to be 11.5% by the Monte Carlo simulation. In identifying A decay, the same selection criteria on the range of the stopping proton and the opening angle between p and ~'- decay particles were imposed as described in Section 3.3. The branching ratio of A ---, p r r - (0.639) was included in the

244

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

50

X 45 o=

: 40

(K-,K*) on SCIFI

INC model

at PK = 1.66 G e V / c

;obbi et of. model

+ I~

t+*,

35 30

%

,I,/o0/f°

25 20 15 10

0

''' 500

600

700

: 800

900

, ,,, IO, ,,, 1000 1100 1200 1300 1400

K÷ momentum (MeV/c)

Fig. 7. The double differential cross sections of (K-, K+ ) reaction (circle) and the sub-threshold fo/ao/fb meson production followed by decaying into K-K+(square). The solid line indicates the intra-nuclear cascade model calculation, while the dashed line shows the calculated result of Gobbi et al.'s [ 14]. r/SFD [24]. Under the selection criteria described in Section 3.1, the background due to K - p --+ ~"°Tr-K+ via the quasi-free ~ * - ( 1 5 3 0 ) resonance was estimated to be about 15% by the Monte Carlo simulation. Other processes carrying invisibly short ~ - decay became negligible after imposing the missing mass criterion. The double differential cross section for f o / a o / f b meson production with subsequent decay to a K - K + pair is shown in Fig. 7. The solid line in the figure represents the result of the INC model calculation, whereas the dotted line represents the prediction by Gobbi et al. The present result is consistent with the prediction of the INC model calculation, while it differs considerably from the result of Gobbi et al. The differential cross section integrated over the momentum region (600 ~< pl¢~ < 950 M e V / c ) was found to be / d~--~L/

=ll+6/zb/sr. A(fo/ao/qS---*K- K + )

The integrated cross section is also consistent with the prediction of the INC model calculation ( ~ 6 /zb/sr). The small discrepancy may be attributable to the K - p -~ f o x °, a0X ° and ~bE° reactions as well as to the lack of experimental data on fo/ao/d? meson production near the threshold energies and the K - K + decay branching ratios of those mesons. However, the differential cross section of Gobbi et al.'s calculation at 600 ~< PK~ < 950 M e V / c is ~ 8 0 /zb/sr, which is an order of magnitude larger than our result. As outlined in the Introduction, the nucleon momentum distribution plays a crucial role in the evaluation of the sub-threshold production of scalar and vector mesons. Gobbi et al. used an "effective incident momentum" to evaluate the effect o f Fermi motion. This brought the maximum K + momentum to 1.1 GeV/c. Nara et al. claim that this method yields incorrect kinematics and overestimates the cross section for scalar and vector meson production [ 15].

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

3=

7 i 6 Two Step Processes r

5 ~.,

~

nC(K-'K*)AAX ,zC(K_,K,)/~_X

.....

"C(K-,K*)Y ~') '#'~X

245

(INC mo~l)

,3

4

2

'

'! 600

" "'-"l" "

,

700

800

,

':i":->.. ....

900 1000 1100 !200 1300 K*momentum (MeV/c)

Fig. 8. The double differential cross sections of two step processes. The closed circles indicate the J2C( K - , K +) A AX reaction, while the squares represent the 12C(K-, K + ) A2?-X reaction. The dashed line shows the INC calculation on the total contribution of 12C( K - , K + ) Y(*)Y{*)X two-step processes.

4.2. Two-step processes The production cross sections for the two-step processes involving two S = - 1 hyperons in the final state, 12C( K - , K + ) YYX, where Y denotes A or 2;:~, were estimated as follows. The double differential cross sections with respect to the final states of the hyperons are shown in Fig. 8. The dotted line represents the INC model calculation for the total contribution of the two-step processes [ 15]. The J 2 C ( K - , K + ) A A X reaction was characterized as consisting of two visible A decays inside the scanning volume. The detection efficiency of the two A decays in the p'lT"-)~lA A. The branching ratio for charged SCIFI target, '~t A s ~, is given by Br2(A particle decay of the AA pair was taken into account by using the factor Br2( A p r r - ) = 0.6392 [24]. The scanning efficiency, rlAA, was deduced from the Monte Carlo simulation based on the real data to reproduce the scanning inefficiency due to the effect of the finite size of the SCIFI detector and short decays of the A particles. The corrected number of events for the I z C ( K - , K ÷ ) A A X reaction is 28/r/SFD aa = 141 ± 27. The differential cross section integrated over the momentum region (600 ~< px, <~ 1300 MeV/c) was found to be ( J-~-[ )

= 17 ± 3.6/zb/sr. t2C(K ,K¢)AAX

This reaction includes 2 ° and 2:* production followed by A7 and A~r° decays, respectively. This cross section is significantly larger than that of the previous DWlA calculation [ 13], which included only 7r as an intermediate meson. Hence, this cross section apparently accounts for the contributions of the {S °, 2"} and other intermediate mesons {r/, w,p}, as well as those of A and ~- [15]. The 12C(K-, K+) A ~ - X reaction was characterized as a visible A decay and a kink

246

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

prong. The efficiency of the SCIFI target, r/SFD, A,~- is given by the product of r/z- and r/A-Br(A ~ p ~ - ) . The scanning efficiency for 27 particles cannot be calculated with the Monte Carlo simulation, because the momentum of 27 cannot be uniquely determined in the present experiment. The efficiency ~7~- was assumed to be similar to ~7.~-, since the lifetime of the 27-(c7" = 4.434 cm) is comparable with that of the = ' - ( c r = 4.91 cm). The number of events favoring the 12C(K-, K +)A27-X hypothesis was found to be seven. This number became 18 + 7 after application of the efficiency correction. The differential cross section integrated over the momentum region (600 ~< Px+ < 950 MeV/c) was found to be ( d~-~L/

= 2 . 3 ± 1.0/zb/sr. 12C( K - , K ~) A.~- X

As for the 12C(K-,K+)27+,Y-X reaction, only one event (PK+ = 880 MeV/c) was clearly identified by two kink tracks from the interaction vertex. The upper limit on the integrated cross section for the 12C ( K - , K +) 2:+ 27- X reaction in the momentum region 600 ~< PK, < 950 MeV/c was estimated by do-

~< No ~ 12C(K-,K+)2.'~.~-X

at 90% C.L.

T]SFD ' ~ S P " T]K~dec

Since the 27~: particles always decay visibly, the detection efficiency r/svD "~: for the t2C(K-, K+)27+X-X reaction is larger than that for the above two reactions, and it was estimated to be 0.64 by the Monte Carlo simulation, assuming pz = 500 MeV/c. The upper limit on the cross section for this reaction was then estimated to be 0.17/xb/sr at a 90% confidence level. The observed cross section for the 12C(K-, K + ) A A X reaction in the momentum region 600 ~< Px, < 950 MeV/c is 9.9 i 2.9 /zb/sr. This value is almost free from contributions of the ~ - - i n d u c e d two-step processes. We stress that the observed cross section is larger than the prediction of Gobbi et al. [ 14]. This result accounts for the role of other intermediate mesons and hyperon resonances decaying into A and other neutral(s). The result of the INC model calculation is consistent with the experimental data regarding production of two hyperons in the momentum region 600 ~< px, < 950 MeV/c [ 15]. However, in the quasi-free ~ - production region, the number of observed AA final states was larger than the prediction of the INC model calculation for the meson-induced two-step processes. The observed cross section for the 1 2 C ( K - , K + ) A A X reaction in the momentum region 950 ~< PK, ~< 1300 MeV/c is 7.1 zk 2.2 /xb/sr, and it is approximately a factor of two larger than the result of the INC model calculation. The INC model calculation predicts that the r/-induced two-step process is dominant in the quasi-free ~ - production region [ 15]. Another possible mechanism for the two A production is the ~ - p --* AA conversion process inside 12C. The total cross section for ~ - p inelastic scattering was deduced from the ='- absorption probability for 12C [23] and nuclear emulsion [25], which are approximately 15 mb and 13 mb at p=- ~ 0.6 GeV/c, respectively. If all the AA productions (7.1 /xb/sr) account for the ~ - - i n d u c e d two-step processes, our results

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250 g.

g

247

50

45

-" Production 40

J~ 2~

35

~2 25 % 2O 15 10

ms t ,,,I .... d.... L,,,,I .... I .... 10,,,I .... 600 700 800 900 1000 1100 1200 1300 1400

Ill 500

K* m o m e n t u m ( M e V / c )

Fig. 9. The double differential cross sections of (K-, K+ ) reaction (circle) and _~*- production followed by _=*- --~ --~r on the SCIFI target (square). indicate a total cross section for the processes to be about 15 mb, assuming an isotropic angular distribution. However, it should be stressed that the INC model calculation [ 15 ] contains uncertainties arising from estimates of the cross sections for the ~TP --~ K +A and K+X ° reactions, which are not known experimentally. Therefore, it is difficult to resolve _~-p --~ AA reaction from other AA production reactions in the ( K - , K +) reaction. Further study is needed to study the _~-p --+ AA reaction. 4.3. Quasi-free _~*-(1530) production Since ~ * - ( 1 5 3 0 ) particle decays completely into the _~7"r state, quasi-free -~*production belongs to either the D-type or Y-type, assuming no _~*N interaction inside 12C. To resolve ~* production out of the ( K - , K +) reactions at low K + momenta, all the known background events were subtracted from the D and Y-type events. These are quasi-free _~- production, fo/ao/fb meson production, and two-step processes, as described in the previous sections. The double differential cross section for _~*production followed by ~ * - ~ ETr on the SCIFI target is shown in Fig. 9. The integrated cross section is 67 dz 8 /zb/sr, which is approximately two thirds as large as the result of the RIA calculation (~95 #b/sr) [ 15]. For 12C, the experimental result is a factor of two smaller than the result of the RIA calculation. However, it should be noted that D and Y-type events contain _~*- production only when the -~*- decays into the ~Tr state without emitting charged tracks longer than 2 mm. Since the RIA calculation does not include the ~ * - interactions inside ~2C, _~*N interactions in ~2C could be a possible explanation for the discrepancy. However, the strengths of the Y*N interactions are not presently known. The observed cross section for the ( K - , K +) reaction on the SCIFI target is 170 ± 7 # b / s r at 600 ~< Px+ < 950 MeV/c. Only two thirds of the events contributing to this cross section are attributed to scalar and vector meson production, the two-step processes

248

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

<

25

>22.5

Other Processes

=o tO

No charged prong 20

Multi-prong

~ 17.5

+

"~-bl2.5 % 10 7.5

,

5 2.5 0

+

, ,,rl,,,,I,,,,I,~,l,,,,I

+ J

....

l,,,,I,,,,I

I ....

5.50 600 650 700 750 800 850 900 g50 1000 K* momentum (MeV/c)

Fig. 10. The double differential cross sections of other processes (circle) which were not identified for the scalar and vector meson production, the two-step processes nor quasi-free ~ - / ~ * - production. The multi-prong (triangle) and no charged prong events (square) of other processes are shown. and quasi-free ~ - / ~ * production, as described in this section. The remaining cross section in this momentum region is on the order of 60/zb/sr, as shown in Fig. 10. The multi-prong events are dominant (39 ± 4 /xb/sr), while the no prong and 1-stop prong events are scarce in the ~ * - production region. The multi-prong events can fill the gap between the RIA result and the experimental data on ~ * - production followed by ~ * - --+ ~Tr. However, the cross section of the elementary process K - p --* ~ * - K + used in the R I A calculation, is inferred from very poor statistics derived from inconsistent data of old bubble chamber experiments [ 21 ]. The multi-prongs from the ( K - , K +) reaction vertex could be due to the secondary interaction o f hyperons in nuclei, including the production and decay of hyperfragments. The probability of observing a single hyperfragment was reported in the hybrid emulsion experiment (KEK-E176). This probability is about 4 ~ 6 % in the momentum region 600 ~< Px+ <~ 900 M e V / c [26]. This corresponds to a cross section on the order of a f e w / z b / s r for the production and decay of a single hyperfragment in ( K - , K + ) reaction on 12C. Of the multi-prong events, 23% were found by eye-scanning to have a A --~ pTrdecay. This represents approximately a half of the multi-prong events after correction for the detection efficiency.

5. C o n c l u s i o n

The ( K - , K +) reaction with the scintillating fiber (SCIFI) active target at pK+ = 1.66 G e V / c was measured to study the reaction mechanism. The ( K - , K +) reaction was identified with the K + spectrometer system covering the angular range 0Lx+ = 2.3 ° to 14.7 °. The SCIFI target with effective volume 8 × 8 × 10 cm 3 allowed us to study the reaction vertex for each event to make further specification of each reaction. We

E224 Collaboration~Nuclear Physics A 625 (1997) 231-250

249

analyzed 2148 ( K - , K +) reaction events for which interaction vertices are located within an appropriate fiducial volume. The events were categorized according to the topology of charged particle tracks observed. By using topological information and kinematical constraints, we identified the events for several reaction processes and obtained the differential cross section for each process. The differential cross section for the sub-threshold scalar (f0 and a0) and vector (&) meson production from 12C followed by K - K + decay was found to be 11 ± 6 /zb/sr at 600 ~< Px+ < 950 MeV/c. This result is consistent with the INC model calculation, while it differs significantly from the calculation of Gobbi et al. The overestimation by Gobbi et al. could be due to their method of approximation of the nucleon Fermi motion, since the sub-threshold production is quite sensitive to the nucleon momentum distribution. The differential cross sections for the 1 2 C ( K - , K + ) A A X and 1 2 C ( K - , K + ) A 2 2 - X reactions were found to be 17±4 and 2.3± 1.0/xb/sr for Px~ ~> 600 MeV/c, respectively. The upper limit on the cross section for the l Zc ( K - , K + ) X - X + X reaction is 0.17/zb/sr at a 90% confidence level. The two-step processes accompanying two S = - 1 hyperons were demonstrated to be sizable in the ( K - , K +) reaction. Comparing with the DWIA calculation, the present result for AA production indicates a large contribution from intermediate heavy mesons (r/, to, p) and hyperon resonances decaying into A and other neutral(s). The experimental values for IZC(K-,K + ) A A X plus 12C(K-, K + ) A S - X are rather close to those given by the INC model calculation for the sum of all the two-step processes, 12C(K-, K+)Y(*)Y(*)X, where Y indicates A or 2~. The observed enhancement of the cross section for AA production compared to the INC model at Px~ ~ 1.1 GeV/c could be due to the E - p --+ AA reaction inside carbon nuclei. If this is the case, the AA resonance search can be performed in the AA mass spectrum from the ( K - , K + ) reaction in the appropriate K + momentum region. The ~ * - (1530) production cross section was estimated to be 67 ± 8 /zb/sr. This is only two thirds as large as the result of the RIA calculation. Since the RIA calculation does not include the ~* interactions in nuclei, E * N interactions in nuclei are a possible explanation for the discrepancy. However, the cross section of the elementary process, K - p ~ ~ * - K +, used in the RIA calculation is inferred from the very poor statistics derived from inconsistent data of old bubble chamber experiments. In order to make a reliable and quantitative study of the E * N interactions in nuclei, one needs much more precise data for the elementary process. We have observed many events which have multi-prongs from the reaction vertex. These are due to the secondary interaction of hyperons and include the production and decay of hyperfragments. Further study is necessary to understand these events.

Acknowledgements We would like to thank the staff of the KEK proton synchrotron for their continuous support. We also thank Professor Y. Akaishi and Dr. Y. Nara for valuable discussions.

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E224 Collaboration~Nuclear Physics A 625 (1997) 2 3 1 - 2 5 0

T h i s w o r k w a s s u p p o r t e d in p a r t b y t h e B a s i c S c i e n c e R e s e a r c h I n s t i t u t e P r o g r a m (BSRI-95-2408),

t h e M i n i s t r y o f E d u c a t i o n , Korea, a n d a G r a n t - i n - A i d for Scientific

R e s e a r c h ( 0 2 4 0 2 0 0 8 ) , t h e M i n i s t r y o f Science, C u l t u r e a n d E d u c a t i o n , Japan.

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A.T.M. Aerts and C.B. Dover, Phys. Rev. D 28 (1983) 450. C.B. Dover and A. Gal, Ann. Phys. 146 (1983) 309. A.J.Baltz, C.B. Dover and D.J. Millener, Phys. Lett. B 123 (1983) 9. R.W. Stotzer et al., to be published in Phys. Rev. Lett. S. Aoki et al., Phys. Rev. Lett. 85 (1990) 1729. J.K. Ahn et al., Phys. Lett. B 378 (1996) 53. PD. Barnes, Nucl. Phys. A 547 (1992) 3c. M. May and G. Franklin, BNL-E885 proposal; L. Lee et al., TRI-PP-94-87 preprint, presented at the Int. Conf. on Hypernuclear and Strange Particle Physics, Vancouver, July 4-8 (1994). [9] S. Aoki et al., to be published in Phys. Lett. B [10] S. Aoki et al., Prog. Theor. Phys. 85 (1991) 1287; K. Imai, Nucl. Phys. A 547 (1992) 199c. [11] G. Burgun et al., Nucl. Phys. B 8 (1968) 447; Dauber et al., Phys. Rev. 179 (1969) 1262; A. De Bellefon et al., Nouv. Cimen. 7 A (1972) 567; Berthon et al., Nouv. Cimen. 21 A (1974) 146; C. Baltay et al., Phys. Rev. D 9 (1974) 49. [12] P.Beilliere et al., Phys. Lett. B 39 (1972) 671; G. Wilquet et al., Phys. Lett. B 57 (1975) 97. [13] T. lijima et al., Nucl. Phys. A 546 (1992) 588. [14] C. Gobbi, C.B. Dover and A. Gal, Phys. Rev. C 50 (1994) 1594. [ 15] Y. Nara, A. Ohnishi, T. Harada and A. Engel, Nucl. Phys. A 614 (1997) 433. [16] J.K. Ahn et al., Nouv. Cimen. 107 A (1994) 2415. [17] J.K. Ahn et al., Nucl. Phys. A 547 (1992) 211c. [18] S. Yamashita, Ph.D. thesis, Kyoto University, KUNS 1332 (1995) (unpublished). [19] Y. Itow, Ph.D. thesis, Kyoto University, KUNS 1362 (1995) (unpublished). [20] Y. ltow et al., to be published in Nucl. Instr. and Meth. A. [211 V. Flaminio, W.G. Moorhead, D.R.O. Morrison, N. Rivoire, Compilation of Cross-Sections II: K + and K - Induced Reactions, CERN-HERA 83-02 (1983). [22] The differential cross section for the K - p --~ K + ~ - process was parametrized to be d g / d f 2 L = 0.66e+4.03 cos o at the angular interval of 0.8 ~< cos 0L ~< 1.0. [23] M.S. Chung, Ph.D. thesis, Korea University, (1995) (unpublished). [24] Particle Date Group, Phys. Rev. D 54 (1996) 1. [25] N. Yasuda et al., to be published in Nucl. Phys. A. [26] M. Iida, M.Sc. thesis, Aichi University of Education, (1996) (unpublished).