c

Nuclear Physics B58 (1973) 178-194. North-Holland Publishing Company

A STUDY OF INCLUSIVE K - p -~ K * -

REACTIONS

K - p '~ k ° + X ° A N D

(890) + X + AT 8.25 GeV/c

Athens - Democritus - Liverpool -

Vienna Collaboration

A. VAYAKI, T.A. FILIPPAS, G.A. GRAMMATIKAKIS, E. SIMOPOULOU and P. TSILIMIGRAS N.R.C. Democritus, Athens

A. ANGELOPOULOS, A. APOSTOLAKIS, P. MICHAELIDES, A. S T E R G I O U and G. VASILIADIS University o f A thens

C. BRANKIN, J.R. FRY, R. MATTHEWS and H. MUIRHEAD University o f Liverpool

D. DALLMAN, P. KATZ and M. MARKYTAN Institut fiir Hochenergiephysik der Oesterr. Akademie der ICissenschaften, Vienna

Received 19 March 1973 Abstract: The inclusive reactions K-p ~ go + Xo and K - p ~ K * - (890) + X+ are studied in detail at 8.25 GeV/c. The most prominent experimental features are discussed in connection with a triple-Regge behavior and, where relevant, compared with the corresponding data of K+p at the same energy. Evidence for pseudoscalar exchange dominance at small t' and low missing mass is suggested by the density matrix element analysis of K*- (890). The natural- and unnatural-paxity contributions to the cross section in the helicity frame indicate characteristics of absorptive behavior.

1. Introduction In this paper we present a study of the inclusive reactions K - p ~ g.° + X° ,

(1)

K - p -+ K * - (890) + X + ,

(2)

produced by 8.25 GeV/c negative kaons interacting in the 2 m CERN Hydrogen Bubble Chamber. Data acquisition and inclusive distributions are presented in sect. 2 and, where relevant, compared with similar data from K÷p at 8.2 GeV/c [1, 2].

179

A. Vayaki et al., Inclusive reactions

The kinematical region of low missing masses and low momentum transfers is examined in sect. 3. In sect. 4 the density matrix elements for K * - (890) decay are used to determine the nature of the exchanged trajectories, and some general predictions of absorptive behavior in the triple Regge region are investigated.

2. Data collection and inclusive distributions The data used for this work consist of 11 855 events with the go seen to decay in the chamber. Corrected for escaping g o _~ n+n- decays and for neutral decay modes, this corresponds to a cross section of 8.6 + 0.6 mb [3]. A strong K * - (890) signal is observed in the K°Tr- effective mass distribution (fig. 1); the K* (1420) resonance is also present. By fitting a Breit-Wigner distribution assuming a polynomial background a cross

K - p - - * R'rr-+ X+ ot

8.25 GeV/c

1600-

1200-

o

800J

0-

.5

1.

1.5

EFF. MASS (K'rr-) Fig. 1. ~ o -

2.0

25

3.0

GeV

effective mass distribution for the reaction K - p -* ~ o -

+ X+ at 8.25 GeV/c.

180

A. Vayaki et aL, lnclusive reactions

Table 1 Compilation of inclusive cross sections for the reactions K - p ~ ~o + Xo, K - p ~ K * - (890) + X+, K+p ~ K° + X++, K+p --+K *+ (890) + X+ Reaction

PLAB (GeV/c)

Cross section (mb)

K-p--+~°+X

8.25 10.02

8.6 -+0.6 7.6 -+ 0.2

K+p ~ K° + X++

5. 8.2

5.86 -+ 0.2 5.86 -+ 0.3

K-p --+K*°,-(890) + X°,+

8.25

3.6 -+ 0.5

8.2

2 . 3 8 -+ 0 . 4

.-~ ~ 0 710, +

K+p ~

K *°' + (890) + X °' +

-~ KOnO, +

section of 2.4 +- 0.3 mb was found [3] for K * - (890) produced in the g o i t - mode. When corrected for the neutral K ° 7r° mode a production cross section of 3.6 • 0.5 mb was obtained. Thus, about 40% of the ~ o originate from the decays K *°'-(890)-~g~°~ ° , - . The same percentage has been found in both K+p at 8.25 GeV/e and K - p at 10 GeV/e experiments [4]. A compilation of the cross sections for K ° and K*(890) at these energies is presented in table 1. To select the sample o f K * - (890) used in the present work a mass cut 0.85 ~
A. Vayaki et al., Inclusive reactions

300;

181

K-p-'-'* K*"(890)÷X ÷ at 8.25 GeVIc

2/,0"

o

180.

0

I J J

e.-

o

Z

120.

60'

1.0

z'.o

3'.0 M (K*)

GeV

Fig. 2. Missing mass distribution to the K*- for the reaction K-p ~ K*- (890) + X+ at 8.25

GeV/c. duality and exoticity (pgO non-exotic, pK ° exotic) more diagrams are contributing to K+pK ° than to K - p K °. In figs. 4 and 5 the distributions da/dt' (t' = I t-tminl) and da/dp~ for ~o and K* (890) are displayed. These distributions as well as the corresponding ones of K+p at 8.2 GeV/c have been fitted in the region of low t' orp;~ with a function of the form BeAz, where z is the appropriate variable, t' or p~. In table 2 the values of A are given both for the K ÷ and K - induced reactions. It is observed that the K induced:reactions have a less steep dependence on t' and p?~ than the K +. A discontinuity is suggested in the t' distribution of the K* at about t' ~ 1 GeV 2 The same feature is also seen in the corresponding K+p data.

A. Vayaki et al., Inclusive reactions

182

cE I0~

"o

"

fit#

2

io-

t

~

t + K- p-.-, P~' + X + K- p --¢ K*-(890) + X+

at 8,25 GeV/c 101 -1.

x=C/ P;,x Fig. 3. Edo/dp ~ versus P~/P~nax distribution for E ° and K * l (890) produced inclusively in K - p at 8.25 GeV/c.

I

+

K-p~P~'+

+

K- p ---, K*-(890) + X +

X

at 8.25 GeV/c

tR÷÷'I'++.F tt~ertt ~ -~-

+tt+tT+++

>. o

tt+

10!

0.

i.

~.

~. t'

~.

GeV 2

Fig. 4. da/dt' distribution for ~o and K*-(890) produced inclusively in K - p at 8.25 GeV/c.

A. Vayaki et al., Inclusive reactions

183

'01 10~: ~t

: ~t~+

K-p--* PJ' + X

K-P ""K*'(890) + X+

at 8.25 GeV/c

A

tO! .-i.

~¢:=.,--- 10~. b

10

o

i.

p2

~. (GeV/c)2

Fig. 5. da/dp~ distribution for ~ o and K * - ( 8 9 0 ) produced inclusively in K - p at 8.25 GeV/c. Table 2 Slopes for do~d(, do/dp~ distributions for the reactions K - p + X + , K + p ._+ K O + X + + , ~K+ p --~ K * + (890) + X+ at 8.25 GeV/e K+p at 8.2

GeV/c

O

K + X °, K - p ~ K * - ( 8 9 0 )

K - p at 8.2 GeV/c

K°

2.3 +- 0.1 GeV - 2

1.7 -+ 0.1 GeV - 2

K*(890)

2.9 -+ 0.1 GeV - 2

2.1 -+ 0.1 GeV - 2

Ko

6.2 -+ 0.2 (GeV/c) - 2

5.6 -+ 0.2 (GeV/c) - 2

K*(890)

4.7 -+ 0.2 (GeV/e) - ~

4.0 -+ 0.2 (GeV/c) - 2

e - A t'

2

e-APT

184

A. Vayaki et al., Inclusive reactions

3. Triple Regge behavior

In this section we shall concentrate in missing masses less than 2.5 GeV. As seen in fig. 6 the signal to background ratio for K*-(890) is very much improved in the region M < 2.5 GeV, t < 1 GeV 2 , thus making an analysis for K*-(890) meaningful. In the scaling limit the triple Regge region is defined for low t, M 2 large and s/M 2 large• Although the c.m. energy of the present experiment (4.07 GeV) is low and s/M 2 not large enough it may be considered that the region M < 2.5 GeV, t' < 1 GeV 2 approaches the triple Regge region at this energy and thus it is interesting to examine our data for features consistent with a triple Regge behavior.

,00

n_

100,,

~

¢u50'/ O c~

0

>~

.

[:.<,

o.v,l 2o0

1 < M < 1.5

~

""In150'

200

IM<2:

G.I

0.15< t'< 0.4

0

i.5 < M < 2.0

® 100.

0.4 < t'< 0.6

100

0 300"

•

IL~

200' I ll 0.6

2 0 < M .,: 2.5

1ooi

0.6 < t ' < 1.0

1:o 1:s 0.8 1:o 1:5 EFF. MASS (~o~_) GeV E F E MASS(K°~r -) GeV Fig. 6. ( p o - ) effective mass distribution for four intervals of t' and four intervals of missing mass in K - p -~ ~ o + lr- + X+ at 8.25 OeV/c.

A. Vayaki et al., Inclusive reactions

185

A simple factorisable triple Regge model predicts the double differential cross section [5] d2o~dtdM =/3(t) y M [ s ]2~(t)- 1 (M2)ff(0)_l '

(3)

where c~ (t) is the exchanged trajectory at the K - K ° ( K - K *) vertex, and ~ ( 0 ) the intercept of an effective trajectory due to the pomeron and normal trajectory exchanged at the proton vertex. As may be seen in fig. 7a the missing mass distribution to the ~o and K * - ( 8 9 0 ) in intervals of t shows a rough linearity when plotted logarithmically, in accordance to the behavior expected from formula (3). In this kinematical region the difference between K + and K - induced reactions can be attributed to interference terms from mixed contributions of vector and tensor exchanges [2] in the triple Regge amplitude. Since the possible natural parity Table 3 Slopes for d 2o/dtdM distributions and value of intercept at M -- 2 GeV for the reactions K - p ~ ~o + Xo, K+p --, Ko + X++ at 8.25 GeV/c

t intervals (GeV2)

K+p --, K° + X at 8.2 GeV/c Intercept at 2 GeV Slope (mb GeV- I )

K-p --*~o + X+ at 8.25 GeV/c Intercept at 2 GeV Slope (mb GeV- 1)

0.05<1t1<0.2

2.2±0J

0.27±0.08

1.7±0.5

0.25±0.08

0.2 < l t l < 0 . 4

4.0±0.9

0.21±0.06

1.7±0.5

0.20±0.06

0.4 < l t l < 0 . 6

3.2±0.7

0.08±0.05

3.4±0.7

0.12±0.06

0.6 < l t l < l . 0

3.2±0.7

0.10±0.05

3.950.7

0.1250.06

Table 4 Slopes for d 2o/dt'dM distributions and value of intercept at M = 2GeV for the reactions K - p ~ K*-(890) + X+, K+p ~ K *+ (890) + X+ at 8.25 GeV/c K+p ~ K*+(890) at X+ at 8.2 GeV/c

K-p ~ K*-(890) + X+ at 8.25 GeV/c

Slope

Intercept at 2 GeV (mb GeV-3)

Slope

Intercept at 2 GeV (rob GeV-3)

0.2~0.1

1.05±0.20

0.3±0.1

1.42±0.20

0.15
0.3±0.1

0.52±0.10

0.6±0.2

0.91±0.15

0.4 < t ' < 0 . 6

0.3~0.1

0.36~0.10

0.6±0.2

0.62±0.15

0.6 < t ' < l . 0

0.6±0.2

0.17±0.05

0.4±0.1

0.43±0.15

t' intervals (GeV2) 0
186

A. Vayaki et al., Inclusive reactions

trajectories (p, A2), (co, f) are exchange degenerate these terms should vanish and the amplitudes for K + and K - should be the same. In this case we expect that the inclusive distributions for g o , K o and K * - , K *+ will be identical. If unnatural parity trajectories are equally present certain terms do not cancel and the distributions are expected to differ. The analysis of K+p for K ° has shown that the energy behavior of the d2o/dtdM cross section is consistent with (p, A2) trajectories for a (t). Lack of energy dependent data does not allow us a separate determination of ~ (t) and ~ ((3). We therefore have to rely on comparison to determine whether our data are consistent with (p, A2) exchanges. In table 3 we give the slopes for ~o and the value of the intercept a t M = 2 GeV. The corresponding values of K ° from K~ at 8.2 GeV/c [2] are also

•

0.05 < I t l < 0 . 2

•

0.2 < l t l < 0 . 4

x

0.4

•

0.6 < Itl <

< Itl < 0.6

K-p--~Ko+X at 8.25 GeV/cl~

1.0

K-p--~ K*('890)+ X+at 8.25 GeV/c

10: 0

%

~0i lo ~.

l ttt t t t

' t

(a) M

GeV

2.0

2.5 1.

M G,!IL-0 ....

Fig. 7. Missing mass distributions to the ~o and K*-(890) produced inclusively in K-p at 8.25 GeV/c. (a) in t intervals; (b) in t' intervals.

187

A. Vayaki et al., Inclusive reactions

shown. Within errors we see that ~o has the same behavior as K °, consistent with (p, A2) exchanges and exchange degenerate trajectories in a triple Regge formulation. As far as the K * - (890) behavior is concerned we observe in fig. 7a that it differs from that of the ~o. The K * - ( 8 9 0 ) distribution at low t is flat. There is a kinematical cut-off at about 2 GeV, imposed by the values of tmin, which are larger for K * - ( 8 9 0 ) than for ~o. As t increases the slope becomes similar to the ~o slopes. In order to compare the K * - ( 8 9 0 ) distributions with the published K+p data at 8.2 GeV/c we again show in fig. 7b the missing mass to the K * - ( 8 9 0 ) now in intervals of t' on a semilog plot +. Due to the missing mass dependence of tmin, the dependence of the double differential cross section on M when t' is the second indeK-p--R°+X at 8.25 GeWc •

$~t

•

K-p~K=+-X*at 8.25 GeV/c t'< 0.15 0.15 < t'< 0.4 x 0 A < t'< 0.6

&0.6 '< t'< 1.0

• ,,~l-~tt~t

,o! tt~ ~tttt~tt~ fflff

i

10! .

]

tt~tttt

t tTtt} [

lO;

10

t/~'~ftttt~| ttttt

f'

titt ,/'""

no

"~ 1( "o

(b)

tt,~,+++

1.

i.

t½tlll*~

M

¢,"

~

tt ~~t

ill -

i.

M

6eV

Fig. 7b.

+ For this distribution only, the K*(890) cross section has been calculated using the microbarn equivalent of the ~o sample, and is again corrected for the neutral mode.

A. Vayaki et al., Inclusive reactions

188

pendent variable is no longer straightforward as in the case of t (formula (3)). Nevertheless, for comparison with K+ we have parametrised the data with a straight line. In table 4 the slopes and the intercept atM = 2 GeV are shown. The slopes do not differ significantly, within errors, while the intercepts are of the same order of magnitude. The intercepts of the K - induced reaction are systematically higher than the K +, but some of this effect may possibly be attributed to differences in the evaluation of the K*(890) cross section in the two experiments.

4. The nature of the exchanged trajectory Some evidence for the nature of the exchanged trajectory in the case of reaction K- p -+ K*- (890) + X÷ may be obtained by the study of the decay angular distriK-p~K*-(890) + X+at 8.25 GeV/c M <1. GeV

20,

1< M<1.5

GeV

1.5<: M<:2.0 GeV

10.

o

Z 40'

2.0<: M<:2.5 GeVfl

30"

10" 0

-I

o

cp

2~

COS e

Fig. 8. Cos 0 and q~decay angles distributions in the G-J frame for the K * - ( 8 9 0 ) resonance produced inclusively in K - p at 8.25 GeV/c. The curves are an evaluation o f the decay f u n c t i o n s using average values o f the density matrix elements.

A. Vayaki et al., Inclusive reactions

189

Table 5 Average values of the density matrix elements in four missing mass intervals for K*(890) decay in the reactions K - p ~ K*-(890) + X+ and K+p ~ K*+(890) + X+ at 8.25 GeV/e Poo

Pl 1

Pl-I

Re PlO

K*-

0.11 ± 0.05

0.45 -+ 0.03

0.38 ± 0.04

0.04 + 0.03

K *+

0.16 ± 0.04

0.42 ± 0.02

0.49 • 0.04

K*-

0.47 ± 0.05

0.27 ± 0.03

0.13 +-0.04

K*+

0.69 +- 0.05

0.16 ± 0.03

0.10 -+0.05

K*-

0.36 ± 0.04

0.32 -+ 0.02

0.14 +-0.04

K*+

0.59 +-0.04

0.21 ± 0.02

0.10 ± 0.04

K*-

0.40 ± 0.03

0.30 -+0.02

0.09 -+0.03

K*÷

0.41 +-0.04

0.30 ± 0.02

0.07 ± 0.02

GeV

M
1
0.05 ± 0.03

1.5

0.04 + 0.03

1.5 < M< 2.0

0.04 + 0.02

2
bution of K * - ( 8 9 0 ) in a suitable frame. We again concentrate in the region M < 2.5 GeV and t' < 1. G¢V 2 where it was seen, fig. 6, that the K * - ( 8 9 0 ) has reduced background. It has been pointed out [6] that for inclusive reactions and for the decay of a vector meson into two pseudoscalar mesons the decay function may be written in the same way as for the quasi two body-case i.e. W (cos 0, ¢) = 3/4n (1/2 (1 - P00) + 1/2 ( 3 P 0 0 - 1) cos 2 0 - p i - 1 sin2 0 cos 2 ¢ - - x / 2 R e P l 0 sin 20 cos¢). We recall that P00 contributes to the unnatural, non-spin-flip cross section, Pl 1 - P l - 1 to unnatural spin-flip and Pll + P l - 1 to natural spin-flip. Fig. 8 gives the cos 0 and ¢ distributions of K* in the G-J frame and for various M intervals. The K * - density matrix elements were calculated by the method of moments, and are shown in table 5 together with the corresponding K *+ values. The curves in fig. 8 are an evaluation of W(O, ¢) using these average values. The obvious change in the shape of the distributions between M < 1 (the quasi two-body reaction K ' p ) and M > 1 suggests a corresponding change in the production mechanism. The p# are displayed in fig. 9a, b as a function of M and for different t' intervals. For all t' and f o r M < 1 GeV (subchannel K ' p ) the p#. values check well with those found in the corresponding exclusive study [7] and indicate a clear dominance of natural parity exchange. For small t' (t' < 0.15 GeV 2) and M > 1 GeV, P00 is above 0.5 but significantly less than 1. We thus find that there is an appreciable contribution of unnatural parity exchange to the non-flip amplitude. The unnatural parity contribution to the spin-flip part given by P l l - P l - 1 is consistent with zero. A small

A. Vayaki et al., Inclusive reactions

190

but non-vanishing contribution of natural parity exchange to the helicity +- 1 of K* is suggested by the value of p 11 +/91-1 and is also consistent with the fact that P00 is smaller than one. With increasing t' cuts 0000 falls below 0.5 and decreases, while 0011 (note that 0000 + 20011 = 1) is seen to increase faster than 001-1- This implies that the unnatural parity contribution to the non-spin-flip part (0000) falls while there is an increasing contribution to the spin-flip part both to the unnatural parity exchange (0011 - / 9 1 - 1) and natural parity exchange (0011 + 001- 1) part of the cross section. We thus arrive at the conclusion that at small t' pseudoscalar exchange dominates. As t' increases other exchanges become prominent. The behavior of K - p ~ K * - ( 8 9 0 ) + X ÷ is in general similar to K+p ~ K*+(890) + X +, as far as the nature of the exchanged trajectory is concerned. There is though a systematic difference in the amount of unnatural parity contribution in the two cases as may be seen in table 5. The K - induced reaction has a K-p~K*-(890) +X+at 8.25 GeV/c E)°° I."

0

t'< 0.15

P1-1

+++++++%++ + 0.15 < t'< 0.4

1."

5. + 0

+£+++-w-_~-~+,

4- 4-

I

. . . . .

0,4 < t < 0.6 1."

.5"

0

1+ 0.6 < t'< 1.0

(a)

5- +4-1-±++++++++ 0

1 ,I

•

I

I.

M

2.

3.

GeV

Fig. 9. Values of the density matrix elements for the K * - ( 8 9 0 ) decay (G-J frame) as a function of a missing mass and for four t' intervals.

A. Vayaki et al., Inclusive reactions

191

smaller value for P00 in missing mass intervals less than 2 GeV, thus exchanges other than pseudoscalar are more prominent in K - than in K ÷. If the triple Regge parametrization of relation (3) is used, the dependence of the double differential cross section for small t, in the case of pion exchange, should be M n. When ~(0) is the intercept of the pomeron, n = 3, while 2 < n < 3 if in addition, the normal trajectory is included. Thus, the flattness of the slope for low t (fig. 7a) cannot be reconciled with a factorizable triple Regge model. Absorptive corrections could introduce a different M dependence. General features of absorptive mechanisms in the triple Regge limit suggest [8] that absorptive corrections to inclusive reactions of the form a + b ~ c + X will give rise to a forward peak in the t' distribution of c when its helicity-flip is zero and a dip in the case of helicity-flip. This is particularly relevant to the case of pion exchange, since if there is no absorption a dip is expected [9]. In order to investigate this behavior we have calculated in the helicity frame the quantities Poodo/dt ', K - p ~ K*-(890) + X+ at 8.25 GeV/c

eu .5"

o

t'
Re

~1o

÷++++-N-+++÷+ t ÷~.p~-~..+..Jr+~+ 0.15 < t ' < 0.4

t

1." .5"

o

+++++++~-~÷÷

++++++++~

0.4 < t ' < 0.6 1." .5'

o

+ ++P--,-H-,-+~

++ ,,,++++-,--!- .-p +

_L i

0.6 < t ' < 1.0

(b)

÷~+÷÷+~ ;. ;. ~.

I- -+~-~.÷-+.~±--~.. ~. 2. 3. M

GeY

A. Vayaki et al., Inclusive reactions

192

103 K-p---,.K~890)

+

X+ot 8.25 GeV/c

1< M<2.5 GeV

I 0:

_~._+

Coo do' / dt"

+

10

? >

.£3

10:

. _ ~ 0.5

~0~ 0.S

1.0

t"

1.0

GeV 2

K-p..-~ K*'IB90) p at 8.25 GeV/c M< I

GeV

x(~l,+ el_,) do"/dt'

~oo do" / dt"

102

10; i

Jo

• (el( ~1-1 ) do" /dt'

101

0 01s t" GeV 2 Fig. 10. Unnatural and natural parity contributions to the cross section for the K * - ( 8 9 0 ) produced inclusively in K - p at 8.25 GeV/c (helicity frame) (a) 1 < M < 2.5 GeV (b) M < 1 GeV. 0.5

A. Vayaki et al., Inclusive reactions

193

(°11 -- P l - l)d°/dt' and (Pll + Pl - 1) d°/dt' for two missing mass intervals, M < 1GeV, I < M < 2.5 GeV. In fig. 10a the unnatural parity contribution to the non-flip part is seen to have a peak at t' = 0, accounting for most of the forward cross section. In contrast, the unnatural and natural contributions to the spin-flip part show no forward peak and are of the same order of magnitude. The unnatural parity contribution is interpreted as indicating pion exchange. Thus, the suggestion that the pion is absorbed when exchanged in inclusive reactions is consistent with our data. In fig. 10b we again observe that the quasi two-body chanuetK*p contrioutes predominantly to the natural parity cross section. The dip seen at t' = 0 has been satisfactorily described elsewhere on the basis of an absorptive model [7]. It is interesting to note that for t' < 0.3 GeV 2 a similar behavior is exhibited by the natural parity contribution in the inclusive channel.

5. Conclusions (i) The inclusive distributions of K ° and K*(890) have a less steep dependence on t' and p~- for K - induced reactions than for K +. (ii) The d2a/dtdM distributions of ~o in K - p exhibit a linearity and are, within errors, identical to the corresponding distributions of K ° in K+p. This is consistent with a triple Regge behavior and exchange degenerate trajectories. (iii) The inclusive K - p -+ K * - ( 8 9 0 ) + X + reaction differs significantly from the exclusive K - p -+ K * - ( 8 9 0 ) p channel, as far as exchanged trajectories are concerned. (iv) Pseudoscalar exchange dominates the forward inclusive K * - ( 8 9 0 ) cross section for low missing masses. Exchanges other than pseudoscalar are more prominent in K - induced reactions than in K + at this energy. (v) The unnatural parity contribution to the non-spin-flip part of the cross section for K * - ( 8 9 0 ) inclusive production has a peak at t' = 0, in contrast to the spin-flip contributions. This suggests that absorptive mechanisms possibly contribute to the pion exchange in this reaction. We would like to thank the scanning measuring and computing staff of each of our laboratories. We are pleased to acknowledge helpful discussions with Drs. V. Goldschmidt-Clermont and W. Kittel. Special thanks are due to Dr. N.'Antoniou for stimulating discussions and his constant interest in this work.

References [1] P. Chliapnikov et al., Nucl. Phys. B37 (1972) 336. [2] P. Chliapnikov et al., Phys. Letters 35B (1971) 581. [ 3] Athens-Democritus-Liverpool-Vienna Collaboration, Cross sections for K-p interactions at 8.25 GeV/c, paper submitted to the Batavia Conf., 1972.

194 [4] Aachen-Berlin-CERN-London-Vienna andBruxelles Collaborations, J.V. Beaupreet al., Nucl. Phys. B30 (1971) 381. [5] D. Horn, Phys. Reports 4 (1972) 1. [6] J.P. Ader et al., Nucl. Phys. B47 (1972) 397. [7] Athens-Democritus-Liverpool-Vienna Collaboration, E. Zevgolatakos et al., Nucl. Phys. B55 (1973) 15. [8] E. Gotsman and U. Maor, Nucl. Phys. B57 (1973) 575. [9] N. Bishari, Phys. Letters 38B (1972) 510.