Experimental characteristics of the charge-exchange K0 producing reactions in K+p and K−p interactions

-] Nuclear Physics B30 (1971) 381-397. North-Holland Publishing Company

EXPERIMENTAL CHARACTERISTICS OF THE CHARGE-EXCHANGE K O PRODUCING REACTIONS IN K+p AND K-p INTERACTIONS Aaehen-Berlin-CERN-bondon-Vienna

and B r u x e l l e s - C E R N C o l l a b o r a t i o n s

J. V. B E A U P R E , M. DEUTSCHMANN, H. G P ~ S S L E R and P. S C H M I T Z 11I. Physikalisches Institut der Technischen Hochschule, Aachen

U. GENSCH, W . D . NOWAK, H . J . S C H R E I B E R and M. W A L T E R Institut pdr Hochenergiephysik der Deutschen Akademie der Wissenschaften zu Berlin, Zeuthen E. DE W O L F , F. GRARD *, P. H E R Q U E T , L. P A P E , P. P E E T E R S , F. V E R B E U R E and R. W I N D M O L D E R S * Laboratoire Interuniversitaire Belge des Hautes Energies, Bruxelles A. A N G E L O P O U L O S **, P. V. C H L I A P N I C O V ***, V. T. COCCONI, O. C Z Y Z E W S K I +, D. D R I J A R D , P. D U I N K E R , W. DUN~IOODIE, A. ESKREYS ++, Y. G O L D S C H M I D T - C L E R M O N T , A. G R A N T , J. D. HANSEN +++, V. P. H E N R I , W. K I T T E L , D. L I N G L I N $, S. MATSUMOTO $~, J. M E Y E R , D. R. O. MORRISON, F. M U L L E R , S. N I E L S E N , Z. S E K E R A and R. STROYNOWSKI CERN, European Organisation f o r Nuclear R e s e a r c h , Geneva P. J. DORNAN, G . A . GRAMMATIKAKIS, B. R. KUMAR and A. M U T A L I B P h y s i c s Department, Imperial College, London B. B U S C H B E C K , A. F R O E H L I C H , P. P O R T H and H. W A H L $:~[ Institut f l i r Hochenergiephysik der (gsterreichischen Akadernie der Wissenschaften, Vienna Received 13 April 1971

* Also at Facult~ des Sciences, Centre Universitaire de l'Etat, Mons. ** Now at the University of Athens. *** Visiting Scientist from the Institute of High Energy Physics, Serpukhov. + Visiting Scientist from the Institute of Nuclear Physics, Cracow. ++ Now at the Ir~stitute of Nuclear Physics, Cracow. +++ Now at the University of Illinois, Urbana, Illinois. :~ Now at the Laboratoire de Physique, Ecole Polytechnique, Paris. :~:~ Visiting Scientist from Chuo University, Tokyo. $ ~ Now Fellow at CERN.

J. V. B e a u p r e et a l . , K ° p r o d u c i n g r e a c t i o n s

382

A b s t r a c t : A study is m a d e of the c h a r g e - e x c h a n g e r e a c t i o n s K+p --* K°X ++ at 5 and 8.2 G e V / c and K-p -* l~°X ° at 10.1 G e V / c , w h e r e X d e n o t e s the s y s t e m of all s e c o n d a r y p a r t i c l e s d i f f e r e n t f r o m K° , with e f f e c t i v e m a s s M. In g e n e r a l it is found that the p r o d u c t i o n p r o p e r t i e s of the K ° and of the X s y s t e m a r e s i m i l a r f o r i n c i d e n t K and K - m e s o n s . The c r o s s s e c t i o n f o r K ° p r o d u c t i o n is ~ 40% of the total i n e l a s t i c Kp c r o s s s e c t i o n in all c a s e s s t u d i e d . The m a s s s p e c t r u m of X, d(r/dM, outside the r e s o n a n c e r e g i o n , i n c r e a s e s e x p o n e n t i a l l y with M , w h i l e the dcr/dt' d i s t r i b u t i o n s d e c r e a s e e x p o n e n t i a l l y as e x p ( - A t ' ) f o r 0 < t' < 1.0 GeV 2, with the value of A depending on the m a s s M as M -°~ (a ~ 2). The s c a l i n g e f f e c t p r e d i c t e d by F e y n m a n is o b s e r v e d f o r the d i s t r i b u t i o n s of x = p ~ / p ~ m a x in the K p r e a c t i o n s at 5 and 8.2 G e V / c . It is shown that a rumple t w o - d l m e n m o n a l p a r r a m e t r i s a t i o n in t e r m s of M and t' can d e s c r i b e s a t i s f a c t o r i l y m o s t of the e x p e r i mental results.

I. I N T R O D U C T I O N In t h i s p a p e r w e p r e s e n t

results

of a study of the reactions _0

-++

K+p-~ l~seenX K-p -~ K°ee n X O ,

,

(1) (2)

produced by 5 and 8.2 GeV/c positive and 10.1 GeV/c negative kaons, interacting in the 150 c m British and 80 c m and 200 c m C E R N hydrogen bubble chambers. The symbol X indicates the system of all secondary particles other than K °. The experimental results on K ° production in reactions (1) and (2) are presented in sect. 2, where w e also derive simple empirical formulae to describe the m a s s M and four-momentum-transfer t' distributions. In sect. 3 a simple overall parametrisation of the data is presented and discussed. Neutral kaons are particles especially well-suited for this type of study, since they are identified easily and observed with little bias, independently of their m o m e n t u m and emission angle. Experiments of this type, often called "inclusive" [1], are to a large extent complementary to the exclusive ones, which study definite final states. A n inclusive bubble chamber investigation is equivalent to a single-arm counter experiment, but has the advantage of covering the full solid angle of particle emission and of studying the contributions to the various effects observed, deriving from final states of different multiplicities. In general the data on the production characteristics of a secondary particle can be presented fully in terms of only two variables. Although several pairs of variables, in principle equivalent, can be used, s o m e choices are m o r e suitable than others for a specific purpose. In this paper w e present the data on K ° production in the form of double-differential cross sections, using several pairs of variables, such as: (a) laboratory m o m e n t u m Plab and laboratory angle 01ab of the K ° mesons; (b) effective m a s s M o f all produced particles other than K ° and squared f o u r - m o m e n t u m transfer (t or t' = = It- tminl) from incoming to outgoing kaon; and (c) normalised longitudinal c.m. m o m e n t u m x = and transverse m o m e n t u m p j_ of the K ° m e -

pL/PLmax

sons.

J. V.'Beaupre et al., IlO producing reactions

383

The data used for this work c o n s i s t of 6 535 events at 5 GeV/c and 10 479 events at 8.2 GeV/e of K+p i n t e r a c t i o n s and of 18 228 events of K-p i n t e r a c t i o n s at 10.1 G e V / c , each event containing a K° o b s e r v e d to decay into two charged pions. The c o r r e s p o n d i n g ~b equivalents a r e 0.29, 0.173 and 0.138 ~ b / e v e n t s , at 5, 8.2 and 10.1 G e V / c , r e s p e c t i v e l y .

2. E X P E R I M E N T A L RESULTS 2.1. C r o s s s e c t i o n s The total n u m b e r of events in which a K° is seen to decay into two charged pions, the total c r o s s section for K° production and the p a r t i a l c r o s s section for channels of different c h a r g e d multiplicities a r e listed in table 1 for the t h r e e e x p e r i m e n t s considered. All K° c r o s s sections a r e c o r r e c t e d for d e c a y s outside the visible region of the c h a m b e r and for unseen decay modes. They a r e obtained by n o r m a l i s i n g the total n u m b e r of events found on a p a r t of the available films ( c o r r e c t e d for scanning l o s s e s ) to the values [2] of the total Kp c r o s s sections listed in the f i r s t row of the table. The values of the inelastic p a r t of the Kp c r o s s sections a r e also listed. As can be seen, the fraction of the inelastic c r o s s section a s s o c i a t e d with K° production ~KO/a.lne is close to 40% for both K+ and K- r e a c t i o n s at the incident m o m e n t a studied. This is essentially true also for r e s u l t s of o t h e r e x p e r i m e n t s at 3 and 3.5 GeV/c (see fig. 1). It is i n t e r e s t i n g to note that a ratio of about 40% is found in the K-p e x p e r i m e n t at 10.1 GeV/c also f o r the ratio an/ainel, which c o r r e s p o n d s to the o t h e r possible c h a r g e exchange r e a c t i o n , K-p--" nX°.

1.0

1

K+p x K- p

•

..i 0.5

b-

o

.

.

.

.

INCIDENT

~ LAB.

.

.

MOMENTUM

.

.

~b ,

'

OeVlc

F i g . 1. R a t i o of K ° p r o d u c t i o n c r o s s s e c t i o n to t o t a l inela+stic c r o s s s e c t i o n a s a f u n c t i o n of i n c i d e n t l a b ~ m o m e n t u m f o r K - p a n d K p i n t e r a c t i o n s .

8-prongs

6-prongs

4-prongs

2-prongs

1230

(~

n u m b e r of e v e n t s w i t h K ° seen

(~

n u m b e r of e v e n t s w i t h K ° seen

1386

n u m b e r of e v e n t s w i t h K ° seen

0.044-0.01mb

16

1.48+0.12mb

4.24m0.20mb

(~

3

±0.05

mb

mb

0.002+0.001 mb

0.27

560

2.40 + 0 . 1 5

3889

3.09 + 0 . 2 1

0.03±0.01 mb

24

0.50+0.04mb

818

2.79±0.18mb

6703

3.66-~0.24mb

9453 mb

mb

7.58+0.18mb

18228

19.4 + 0 . 2

n u m b e r of e v e n t s w i t h K ° seen

6027

mb

mb

mb

GeV/c

0.60+0.06 mb 5133

5.76 + 0 . 3 3

10479

+0.3

22.5 -~0.2

K - p at 10.1

(~

n u m b e r of e v e n t s w i t h K ° seen

5.76+0.21mb

total c r o s s s e c t i o n f o r K° p r o d . , (~Ko

0-prongs

6535

13.8

mb

13.6 + 0 . 3

mb

17.2

mb

17.2 + 0 . 2

-~0.1

K+p at 8.2 G e V / c

K+p at 5 G e V / c

total n u m b e r of e v e n t s w i t h K ° seen

(~inel (Kp)

fftot (Kp)

Reaction

Table 1 Total and p a r t i a l K ° c r o s s s e c t i o n s , and n u m b e r of e v e n t s f o r the r e a c t i o n s (1) and (2). All K ° c r o s s s e c t i o n s a r e c o r r e c t e d f o r u n s e e n K ° d e c a y m o d e s and f o r d e c a y s o u t s i d e t h e c h a m b e r .

¢5

~5

J. V. Beaupre et al., II ° producing reactions

385

2.2. D i f f e r e n t i a l - c r o s s - s e c t i o n distributions In fig. 2 we p r e s e n t t h e d 2 ~ / d P l a b d ~ 2 1 a b d i s t r i b u t i o n s , a s f u n c t i o n s of P l a b , f o r v a r i o u s i n t e r v a l s of the e m i s s i o n a n g l e 01a b. T h e e v e n t s w e r e w e i g h t e d b y t h e f a c t o r (2n s i n 0 l a b ) - 1 , w h i c h t a k e s into a c c o u n t t h e s u m m a tion over relatively large solid angles. A s t r u c t u r e i s s e e n n e a r the m a x i m u m P l a b f o r s m a l l a n g l e s in K+p r e a c t i o n s . T h i s i s a c o n s e q u e n c e of &++ p r o d u c t i o n . On the o t h e r hand t h e r e i s no d e f i n i t e e v i d e n c e f o r an e n h a n c e m e n t c o r r e s p o n d i n g to &o p r o d u c t i o n in K - p i n t e r a c t i o n s , p r e s u m a b l y b e c a u s e t h e c o r r e s o o n d i n g s m a l l p e a k i s m a s k e d by N *° p r o d u c t i o n . T h e l a b o r a t o r y - m o m e n t u m d i s t r i b u t i o n s of a l l the K ° m e s o n s shown in fig. 3 p r e s e n t the s a m e f e a t u r e .

2.3. The P L and p± distributions R e c e n t l y F e y n m a n I l l a d v o c a t e d the p r e s e n t a t i o n of h i g h - e n e r g y d a t a in J * * 2 • • • t e r m s of t h e v a r i a b l e s x = P L / P L m a x a n d p±. The d t s t r z b u t m n s of x f o r the K°_ m e s o n s in r e a c t i o n s (1) and (2) a r e shown in fig. 4. W e s e e t h a t K + and K d a t a a r e s i m i l a r in s h a p e . The d i s t r i b u t i o n s a r e a s y m m e t r i c a r o u n d the a x i s x = 0; d ~ / d x d e c r e a s e s r a p i d l y w i t h i n c r e a s i n g n e g a t i v e v a l u e s of x and much more slowly for positive x values.

K+p"~Ke+X ÷÷

AT 8 . 2 i

GeV/c

K-p~K%

A T 10.1 GeVlc

Xe

i & (1236)

lO 5

I

eLA B

, mr

5z~

f

10 3

"

so

-¢-

¢-

•o

2o-

20

lo=

~ I

÷

+

+

101 -

.~-

.+.

e,

t +

i

÷

.

¢

+ 4e

+

+

50-

100

loo-

2oo

200 - 300

t.

~,

300 - 500

1L

700 -1000

500 - 700

+

÷ lOOO

t

'!t

~

±

°

.

_

/ 10-1 o

,

r

l

,

,

,

5

5 PLAB

lO

" GeVlc

Fig. 2. Double-differential c r o s s - s e c t i o n distribution d2a/dPlab d ~ l a b for K° mesons produced in reactions (1) and (2}.

J. V.Beaupre et al., K ° producing reactions

386

i

1500

i

,

!

, ~

K'l'p _.~.K°+ X ÷+

tl,'r

AT 8.2 GeVlc

/

i

1+, I

/

'~

o'I

,

~

=..

j

:i

I

K- p_.,. i~+ X °

|111

,soo

AT 10.1 GeVlc

'"

,ooo /

2 K° LAB.

4

6

MOMENTUM,

8

10

PLAB ' GeVIc

Fig. 3. K° lab momentum distributions for K+ and K- interactions. The lines r e p r e s e n t the predictions of the p a r a m e t r i s a t i o n described in sect. 3. The solid lines are for the fitted region, the dotted lines for the extrapolation.

T h e s e d a / d x d i s t r i b u t i o n s f o r K° m a y b e c o m p a r e d w i t h t h o s e o b t a i n e d f o r p r o t o n s [3] and p i o n s [4] p r o d u c e d in pp i n t e r a c t i o n s . F o r p r o t o n s , dg/dx is essentially flat, while for pions it decreases rapidly with increasi n g I x ] . T h u s , K ° m e s o n s p r e s e n t a b e h a v i o u r i n t e r m e d i a t e b e t w e e n t h a t of p r o t o n s and p i o n s , i . e . , t h e y t e n d to k e e p t h e m o m e n t u m of the i n c i d e n t p a r t i c l e , b u t to a s m a l l e r e x t e n t than the p r o t o n s . It i s i n t e r e s t i n g to n o t e in fig. 4b t h a t the d a / d x d i s t r i b u t i o n s f o r r e a c t i o n (1) a t 5 and 8.2 G e V / c a r e not o n l y s i m i l a r , b u t p r a c t i c a l l y i d e n t i c a l a l s o in a b s o l u t e v a l u e (no n o r m a l i s a t i o n w a s m a d e ) , a t l e a s t f o r - 0 . 5 < x < +0.7. T h i s m a y be t a k e n a s e v i d e n c e f o r the s c a l i n g b e h a v i o u r p r e d i c t e d by F e y n m a n [1], i . e . d ~ / d x d i s t r i b u t i o n s a r e e n e r g y i n d e p e n d e n t , at l e a s t b e t w e e n 5 and 8.2 G e V / c f o r K+p i n t e r a c t i o n s . In fig. 5 we p r e s e n t the d i s t r i b u t i o n of d~/dP 2 f o r K° m e s o n s . The e x p e r i m e n t a l r e s u l t s can b e d e s c r i b e d s a t i s f a c t o r i l y b o t h by an e x p o n e n t i a l f u n c t i o n o f p 2 and by t h e C o c c o n i - K o e s t e r - P e r k i n s f o r m u l a [5] in the r e g i o n of p 2 ..< 0.5 ( G e V / c ) 2, w h i c h c o n t a i n s the g r e a t m a j o r i t y of the e v e n t s .

387

J. V. Beaupre et al., K ° producing reactions 10 5

i

i

• K-p~KO÷X ° "

i

i

AT 10.1 GeVlc

K÷p --,.. K% X'H" AT 8 . 2

K+p~

GeVlc

•

104

f.

JQ :Z_

5

GeVlc

- 8.2

GeV/c

--,,.

b

'1o

i

j

?

10 3

i

K°+ X++

'+4

10 2

t

101

-1.0

I

-0.5

I

I

0

-~0.5

x = PL'/

I

-1.0

P:MAX

FOR

-0.5

I

0

t

÷0.5

+lJ

K°

F i g . 4. D i s t r i b u t i o n of d g / d x , w h e r e x i s t h e e . m . l o n g i t u d i n a l m o m e n t u m o ~ t h e K° m e s o n divided by the m a x i m u m a v a i l a b l e m o m e n t u m .

2.4. M i s s i n g m a s s s p e c t r a F i g . 6 s h o w s in a s e m i - l o g a r i t h m i c p l o t the m a s s s p e c t r u m of the s y s t e m X in r e a c t i o n s (1) and (2). F o r low m a s s e s of X, e n h a n c e m e n t s a r e o b s e r v e d w h i c h a r e d u e to p r o d u c t i o n of b a r y o n i c r e s o n a n c e s . A t h i g h e r m a s s e s , a b o v e a b o u t 2.0 GeV, h o w e v e r , i t can b e s e e n t h a t the d i s t r i b u t i o n s a r e e s s e n t i a l l y s m o o t h and c o n s i s t e n t w i t h an e x p o n e n t i a l s h a p e . T h i s h i g h e r m a s s r e g i o n can b e f i t t e d w i t h t h e f o r m u l a d~ dM-

kM

~o e

(3)

The v a l u e s of t h e f i t t e d s l o p e k and of the n o r m a l i s a t i o n c o n s t a n t % , a s w e l l a s the M - r e g i o n o v e r w h i c h f o r m u l a (3) w a s f i t t e d , a r e given in t a b l e 2. T h e s a m e p r o c e d u r e w a s r e p e a t e d f o r e v e n t s w i t h t ' ~< 1.0 GeV 2 and the r e s u l t s a r e a l s o g i v e n in the t a b l e . In a l l t h e t h r e e c a s e s i n v e s t i g a t e d the s l o p e k f o r the t o t a l s a m p l e of e v e n t s h a s a v a l u e b e t w e e n 1.6 and 2.1 G e V - 1 ; f o r e v e n t s w i t h t ' --< 1.0 GeV 2 t h e v a l u e of k i s s o m e w h a t l o w e r and v a r i e s b e t w e e n 1.3 and 1.8 GeV -1. T h e r e i s a t e n d e n c y f o r t h e v a l u e of k to d e c r e a s e when the i n c o m i n g e n e r g y increases. T h e f a c t t h a t t h e m a s s s p e c t r u m of t h e s y s t e m X i s e x p o n e n t i a l i s s u r p r i s i n g s i n c e t h i s d i s t r i b u t i o n i s a s u p e r p o s i t i o n of a l l the s p e c t r a c o r r e s p o n d i n g to t h e v a r i o u s m u l t i p l i c i t i e s in the f i n a l s t a t e , w h i c h , a s can b e s e e n in fig. 7 f o r s o m e e x a m p l e s of 4C a n d 1C f i t t e d c h a n n e l s , i n d i v i d u a l l y a r e by no m e a n s e x p o n e n t i a l and d i f f e r v e r y m u c h a m o n g t h e m s e l v e s . In o r d e r to s t u d y in m o r e d e t a i l the m a s s d i s t r i b u t i o n of the s y s t e m X

J. V. Beaupre et al., K ° producing reactions

388

Table 2 Fitted coefficients in f o r m u l a (3), d(~/dM = (~o e k M . Reaction

Mass range

t ' range

(lo

k

× 2 / d e g r e e s of

(GeV)

(GeV 2)

(/2b/GeV)

(GeV -1)

freedom

All

40.6 ± 2.0

2.10±0.05

21/8

0-1.0

49.6±2.4

1.81±0.05

32/8

All

17.1 ± 0.8

1.70 ± 0,05

47/27

0-1.0

44.3±2.1

1.33±0.05

36/27

All

19.1±0.9

1.65±0.05

42/34

0-1.0

34.1±1.7

1.31±0.05

42/34

K+p_, KOx++ at 5 GeV/c

2 . 0 - 2.5

K+p --, KOx++ at 8.2 G e V / c

2 . 0 - 3.45

K - p ~ ~-OxO at 10.1 GeV/c

2.0-3.8

l0~ 104

K*p .-. 'K~-X +÷ AT 8.2 GeVIc

,o'

"....÷

103

~

10 4

-4-+..I_

÷+.

t02 O

=L

I

l0 s

0!1

I

I

K-p_.R°x

o AT 10.1 GeVIc m

0

5.10~

o.

b "O 103

-t-

-I-

o

10 2

o!,

~

++--F--

+ 10

0

0'.5

I'.0

I'.5

210

215

PI OF K°, (GeVlc) 2 Fig. 5. T r a n s v e r s e m o m e n t u m squared d i s t r i b u t i o n of K°.

389

J. V.Beaupre et al., K ° producing reactions !

i

104

:'

I

x

~

~

,0 2

j-

+ .,~7" .l~kt~

>

i01

~r

10~

K ' p ~ K% X"÷

i

~.~+"

:

i

K*p--K%X*+ AT 5 C'e'c"

103

~*

I

i

.I

~

_

I Kp-

R%xo

AT 10.1GeV/c

+ fl'~ -I

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.

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F i g . 7. M i s s i n g m a s s d i s t r i b u t i o n s dcr/dM f o r d i f f e r e n t m u l t i p l i c i t i e s in t h e f i n a l s t a t e .

~; -2 5 d e c r e a s e s w i t h i n c r e a s i n g ' przmary" m o m e n t u m a p p r o x i m a t e l y a s Plab" ' s i m i l a r l y to w h a t i s o b s e r v e d f o r t w o - b o d y c h a r g e - e x c h a n g e r e a c t i o n s [7].

2.5. F o u r - m o m e n t u m - t r a n s f e r distributions In fig. 8 a r e shown the d v / d t d i s t r i b u t i o n s of K ° f o r b o t h K - and K + i n c i d e n t p a r t i c l e s , and in fig. 9 the d~/dt' d i s t r i b u t i o n s . It m a y b e s e e n t h a t the g e n e r a l s h a p e of t h e t and t ' d i s t r i b u t i o n s of the K ° m e s o n s p r o d u c e d in K and K + i n t e r a c t i o n s a r e s i m i l a r and g r e a t l y a t v a r i a n c e w i t h p h a s e s p a c e p r e d i c t i o n s ( d a s h e d l i n e s in fig. 9) in the r e g i o n 0 < t ' < 2.0 GeV 2 w h i c h c o n t a i n s 80% of t h e e v e n t s . The t ' d i s t r i b u t i o n s f o r d i f f e r e n t m a s s b a n d s of X a r e p r e s e n t e d in fig. 10. In the s m a l l t ' (t' ~< 1.0 GeV 2) r e g i o n they a r e c o n s i s t e n t w i t h the e x p o n e n tial (dt-~a,)M = e ° n s t = ( c o n s t , e - A t '

(4,

-2.5 P r e l i m i n a r y r e s u l t s for 16 GeV/c K+p interactions confirm this Plab dependence.

J. V. Beaupre et al., Ii ° producing reactions

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A = c(~---~)-a

Mo = l GeV

(5)

and v a l u e s of c = 2 6 . 4 + 2 . 5 GeV -2 and of a = 2 . 3 4 + 0 . 1 2 w e r e o b t a i n e d . It i s known t h a t 7r+p i n t e r a c t i o n s a t 8 G e V / c can b e w e l l d e s c r i b e d by a s i m p l e m o d e l w h e r e t h e t r a n s i t i o n m a t r i x e l e m e n t d e p e n d s o n l y on the f o u r -

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J. Y'.Beaupre et a l . , K ° p r o d u c i n g r e a c t i o n s

393 ,

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Fig. 10. The t' = It - t m i n 1 distributions of K° for different m a s s bands of the system X. as p r o d u c e d a l o n e at o n e i n t e r a c t i o n v e r t e x not c o r r e l a t e d w i t h the p a r t i c i e s c o n t a i n e d in the X - s y s t e m . T h i s d o e s not, o b v i o u s l y , c o r r e s p o n d to r e a l i t y . In p a r t i c u l a r , an i m p o r t a n t f r a c t i o n of the K u m e s o n s m u s t a e r i v e f r o m the d e c a y of K* r e s o n a n c e s . In fig. 12 a r e p r e s e n t e d the (K°~ +) e f f e c t i v e - m a s s s p e c t r u m f o r r e a c t i o n ( 1 ) a n d the (K'°~ -) e f f e c t i v e m a s s s p e c t r u m for r e a c tion (2). In both d i s t r i b u t i o n s o n e can s e e a s t r o n g K*(890) p~ak, that i n c l u d e s about 25% of the K° m e s o n s . W e e s t i m a t e d that, in total about 40% of the K- m e s o n s p r o d u c e d at 8 to 10 G e V / c d e r i v e f r o m the k~own K* r e s o n a n c e s , both in c h a r g e d and n e u t r a l s t a t e s . S i n c e K*(890) g i v e s the l a r g e s t c o n t r i b u t i o n , w e have v e r i f i e d that the g e n e r a l b e h a v i o u r of the K° d e r i v i n g f r o m the K*(890) m a s s band i s s i m i l a r to the b e h a v i o u r of the K° f r o m m a s s

J. V. Beaupre et al., K ° producing reactions

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b a n d s a d j a c e n t to K*(890) in the (K°n) s y s t e m . T h e r e f o r e , w e c o n c l u d e t h a t the g e n e r a l b e h a v i o u r of t h e K° i s not g r e a t l y a f f e c t e d by r e s o n a n c e p r o d u c tion.

3. P A R A M E T R I S A T I O N O F THE D A T A W e h a v e shown t h a t f o r s m a l l t ' v a l u e s (t' --< 1.0 GeV2), the t ' d e p e n d e n c e of the c r o s s s e c t i o n f o r e a c h n a r r o w b a n d of t h e m a s s M i s d e s c r i b e d by the e m p i r i c a l f o r m u l a (3), and t h e M - d e p e n d e n c e of the e x p o n e n t i a l s l o p e A i s d e s c r i b e d by t h e f u n c t i o n (5). A s o n e can s e e in fig. 10, t h e t ' d i s t r i b u t i o n i s w e l l d e s c r i b e d by o u r e x p o n e n t i a l f i t s a l s o f o r t ' v a l u e s s o m e w h a t l a r g e r than 1.0 GeV 2. T h e r e f o r e w e c a n t r y to e x t e n d o u r p a r a m e t r i s a t i o n o v e r the whole kinematically allowed region. The double differential cross section m a y then b e w r i t t e n in t h e f o r m : dt' dM - f(M) exp F o r m u l a (3), w h i c h g i v e s the d a / d M p a r ~ m e t r i s a t i o n , i s the r e s u l t of t h e i n t e g r a t i o n of f o r m u l a (7) o v e r t ' --< 1.0 GeV "~. C o m b i n i n g f o r m u l a e (3) and (7) w e g e t :

J . V . B e a u p r e et a l . , K ° p r o d u c i n g r e a c t i o n s

395

1000 - - (K%'-) EFF. MASS IN K-p AT 10.1 GeVlc

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i

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F i g . 13. T w o - d i m e n s i o n a l p l o t of t ' v e r s u s M f o r all K° e v e n t s in r e a c t i o n s (1) and (2). The s o l i d l i n e s d e l i m i t the r e g i o n in w h i c h f o r m u l a e (3) and (4) have b e e n f i t t e d to the d a t a . The d a s h e d l i n e s r e p r e s e n t the k i n e m a t i c l i m i t s .

J. V. Beaupre et al., K ° producing reactions

396

d2~ /M\ d r ' d M - (ro c ~ o }

-a

exp[kM-c(M/Mo)-at 1 - exp [-c(M/Mo)-a~

'] ,

(8)

where the parameters go and k are the constants given in table 2. The region of strict validity of this formula is limited to the same range of M as for eq. (3), i.e. 2.0 -2.5 GeV and 2.0-3.45 GeV for K+p reactions at 5 and 8.2 GeV/c, respectively, and 2.0 - 3.8 GeV for 10.1 GeV/c K-p reactions. The limits of strict validity of the parametrisations are shown in fig. 13 by the solid lines delimiting rectangular regions in the plots of M versus t'. Though these rectangles cover a small fraction of the kinematically allowed areas, the events are strongly concentrated in the region of large M and small t ' , so that, for both K+ and K- reactions, the rectangles contain approximately 50~ of the total events. As an example of the accuracy of the parametrisation of eq. (8) in describing the data, we show in fig. 3 the calculated distribution of dg/dPla b. The curve is drawn as a solid line for the /blab region where eq. (8) is strictly valid and as a dotted line for the extrapolated regions. As can be seen in fig. 3, the solid line covers a very small range of ,blab and the extrapolations at high momenta and at low momenta down to about 2 GeV/c satisfactory describe about 80~oof the events. Disagreement is noted, however, specially in fig. 3a, in the high momentum range, at the values of/bla b which correspond to baryonic resonances production (mostly A(1236)). Besides, for momenta below ~ 2 GeV/c, the parametrisation is definitely inadequate; this region corresponds to KU mesons produced backwards in the c.m. system. All the other experimental distributions presented in this paper have been compared with the predictions of parametrisation (8). The results are not shown here, because the situation is always the same as described for fig. 3, namely that the description is adequate, except for baryonic resonance production and backward emitted K° mesons.

6. CONCLUSIONS In the s t u d y of 5 and 8.2 G e V / c K+p and 10.1 G e V / c K - p i n t e r a c t i o n s c o n t a i n i n g a K ° in the f i n a l s t a t e p l u s the s y s t e m X of any o t h e r p a r t i c l e s , the following results were obtained: (a) T h e r e i s no q u a l i t a t i v e d i f f e r e n c e , a p a r t f r o m a b s o l u t e c r o s s s e c t i o n s , in the p r o d u c t i o n c h a r a c t e r i s t i c of K° by K - and K + m e s o n s . (b) T h e r e i s no s t r o n g e n e r g y d e p e n d e n c e f o r the p r o b a b i l i t y of t h e i n e l a s t i c c h a r g e - e x c h a n g e r e a c t i o n s , i . e . , the f r a c t i o n of the i n e l a s t i c r e a c t i o n s g i v i n g K ° m e s o n s i s a p p r o x i m a t e l y c o n s t a n t b e t w e e n 3 and 10 G e V / c and e q u a l to a b o u t 40% of t h e t o t a l i n e l a s t i c c r o s s s e c t i o n . (c) The d i s t r i b u t i o n of the e f f e c t i v e m a s s of the s y s t e m X i s e x p o n e n t i a l f o r M >/ 2.0 G e V , in a l l c a s e s s t u d i e d . (d) The dcr/dt' d i s t r i b u t i o n s f o r a g i v e n b a n d of the m a s s of X can b e f i t t e d , f o r s m a l l t ' v a l u e s , w i t h an e x p o n e n t i a l exp ( - A t ' ) ; the p a r a m e t e r A of the e x p o n e n t i a l d e c r e a s e s w i t h i n c r e a s i n g v a l u e s of the m a s s a s

V.

Beaufire et al., P pmducirg reactious M

-ct

(M,>

’

397

with (r = 2.

(e) For a fixed band of M, we observe a strong energy dependence of the cross section, which in the range from 5 to 10 GeV/c decreases with the increasing primary momentum approximately as fiitb5, similarly to what is observed for two-body charge-exchange reactions. (f) The values of the parameter A of the do/dt’ distributions are much larger than those expected from the peripheral production of nucleons. (g) The production of K* resonances does not affect significantly the general behaviour of the K” mesons. (h) About 80% of the data are reasonably described by the two-dimensional parametrisation in t’ and M given by eq. (8), deduced from fits describing about 50% of the events. It would be of great interest to compare these results with the limiting fragmentation model [9], Feynman’s ideas [l] or the thermodynamical model of Hagedorn [lo]. Unfortunately, at present, these predictions are not available in a form which may be directly compared with our experimental data. We are indebted to the operating crews of the CERN proton-synchrotron, 150 cm British, 80 cm and 200 cm CERN hydrogen bubble chambers and to the constructors of the beams. We would like to thank the scanning, measuring and computing staff of each of our laboratories. We are pleased to acknowledge helpful discussions with Dr. R. Armenteros and Professor Ch. Peyrou. REFERENCES [l] R.P.Feynman, Phys. Rev. Letters 23 (1969) 1415. [2] R.L.Cool et al., Phys. Rev. Letters 17 (1966) 102; W. Galbraith et al., Phys. Rev. 138 (1965) 913; E. Flaminio, J.D. Hansen, D. R. 0. Morrison and N. Tovey, Compilation of cross sections, CERN/HERA reports 70-6, 70-7. [3] E.W.Anderson et al., Phys. Rev. Letters 19 (1967) 198. [4] H. Bdggild et al., Scandinavian Bubble Chamber Collaboration, ‘Nucl. Phys. B27 (1971) 285. [5] G. Cocconi, L. J. Koester and D. H. Perkins, UCRL 10022 (1961) p. 187. [6] J. Barthe, Statistical model and cross sections for high-energy reactions, Herceg-Novi report (1970). [7] D. R. 0. Morrison, Phys. Letters 22 (1966) 528. [8] T.Hofmokl et al., Nucl, Phys. B4 (1968) 573.: [9] J.Beneche, T. T. Chou, C. N.Yang and E.Yen’, Phys. Rev. 188 (1969) 2153; H. Cheng and T. T. Wu, Phys. Rev. Letters 23 (1969) 1311. [lo] R.Hagedorn, Nuovo Cimento 56A (1968) 1027.