Volume 39B, number 4 P H Y S I C S L E T T E R S 15 May 1972

D E T E R M I N A T I O N O F T H E K s ° D E C A Y B R A N C H I N G R A T I O

J. A L I T T I , E. LESQUOY, A. M U L L E R D~partement de Fhysique des Part icules El~mentaires , CEN - Saclay, France

Received 27 March 1972

Using K° 's . reduced in K+p interactions at 1.4 GeV/c in hydrogen we have measured the branching ratio (K°s -. 7r+rt-)/(K°s--Tr°Tr° ). Our result 2.22 + 0.10 is in good agreement with the average of ea r l i e r experiments.

We u s e d about 55 000 two p rong and two p r o n g +V ° i n t e r a c t i o n s o b s e r v e d in a 1.4 G e V / c K + b e a m e x p o s u r e with the C E R N 2m h y d r o g e n bubble c h a m b e r . F r o m the a n a l y s i s of a l l e v e n t s t r e a t e d as two p rong e v e n t s we ob ta in the to ta l n u m b e r of K ° ' s p r o d u c e d by the r e a c t i o n K + + p ~ p + ~+ + + K o. The n u m b e r of I~s-~n+Tr- i s ob ta ined by

o decay . The r a t io (K~ ~u+Tr-) / o b s e r v i n g the K s (K°s ~ 7r°~ °) i s deduced f r o m the m e a s u r e d r a t i o (K o ~ , + u - ) / K ° to ta l .

Al l two p rong e v e n t s have been s canned with a r e q u i r e m e n t of a m i n i m u m s e c o n d a r y t r a c k l eng th of 3mm. F o r each even t the s c a n n e r s looked fo r a V ° topology in a decay v o l u m e s u r - rounding the p r o d u c t i o n v e r t e x . No r e j e c t i o n c r i t e r i a w e r e app l i ed to th is V ° . Two c o m p l e t e s c a n s have been p e r f o r m e d .

The m e a s u r e m e n t s w e r e done on the SACLAY HPD I work ing in a fu l l qu idance mode . A f t e r g e o m e t r y the f r a c t i o n of r e j e c t e d e v e n t s due to a f a i l u r e on one s e c o n d a r y t r a c k f r o m the p r o d u c - t ion v e r t e x is (6.6 • 0.1)% fo r the two p rong ( fo r - w a r d e l a s t i c e v e n t s have been r e m o v e d ) and (6.9 ± 0.9)% for two p rong + V e v e n t s 1).

I gno r ing the V o, the fo l lowing k i n e m a t i c f i t s w e r e t r i ed : K + + p ~ K + + p (1)

K + + p + r. ° (2) ~r + + p + K ° (3)

~ K + + u++ n. (4) The p robab i l i t y cut was se t at 1%. E v e n t s f i t -

t ing r e a c t i o n (1) w e r e r e m o v e d . A f t e r i on i za t i on i n spec t i on , only u n a m b i g u o u s e v e n t s of r e a c t i o n (3) w e r e r e t a i n e d 2). The s e l e c t e d e v e n t s with an

1) This shows that the vicinity of a V ° does not impair significantly the fi l tering of the secondary tracks.

2) The respective cross sections at 1.4 GeV/c for re- actions (1), (2), (3), (4) are 10rob, 2 rob, 5.4rob, 0.8 rob; additional pion production in the two prong topology is ~ 2% of reaction (3).

o b s e r v e d V ° cand ida t e w e r e r e m e a s u r e d on c o n - ven t iona l m e a s u r i n g m a c h i n e s . V e r t e x a s s o c i a - t ion was t r i e d and a l s o the K ° ~ n+n- decay . A f t e r s e v e r a l m e a s u r e m e n t s and p i c t u r e i n s p e c - t ion we e x t r a c t e d the K ° - ~+n- d e c a y s , e v e n if the c o m p l e t e 7C fi t fa i led .

The K~s -n+n- s y s t e m a t i c l o s s e s both at the scann ing and m e a s u r i n g l e v e l have been d e t e r - m i n e d by looking at the t so t ropy of the two decay ang l e s , and w e r e found to be (0.71 + 0.07)%. The r a n d o m scann ing l o s s e s r e m a i n i n g a f t e r two s c a n s a r e neg l i g ib l e , the scann ing e f f i c i e n c y be ing 99.85% for two p r o n g s and 99.81% f o r two p rong + V even t s .

The n+ b e a m c o n t a m i n a t i o n m e a s u r e d th rough b a c k w a r d e l a s t i c s c a t t e r i n g was found to be (0.25 :L 0.05)%. No c o r r e c t i o n has t h e r e f o r e b e e n m a d e for n + i n e l a s t i c e v e n t s f i t t ing r e a c - t ion (3).

K ° s c a t t e r i n g , K~s r e g e n e r a t i o n , t h r e e body K ° l ep ton ic d e c a y s faking K ° ~ ~+Tr- a r e c o m - p l e t e ly neg l i g ib l e in our decay v o l u m e wi th in o u r s t a t i s t i c s .

In a s econd s tep a m i n i m u m p r o j e c t e d decay leng th o f . , m m was r e q u i r e d and the decay v o l - u m e was r e d u c e d ; each V ° has b e e n we igh ted by the usua l d e t e c t i o n p robab i l i t y . The s a m p l e of two p rong e v e n t s was c o r r e c t e d to accoun t fo r the p r o b a b i l i t y of the V ° decay ing ou t s i de the decay vo lume .

Tak ing only the f i t t ed K ° p a r a m e t e r s f r o m the 1C fit for both t o p o l o g i e s , the d e t e c t i o n p r o b a b i l - i ty has b e e n r e c a l c u l a t e d and a l l e v e n t s wi th th is we igh t b i g g e r than 1.3 have been r e m o v e d . T h i s cut a v o i d s m o r e c o m p l i c a t e d c r i t e r i a on s m a l l m o m e n t a , s m a l l po t en t i a l l eng th and l a r g e dip angle .

In o u r f inal s a m p l e we r e m a i n with 9979 e v e n t s of r e a c t i o n (3) of which 3068 have a v i s i b l e K ° :~ ~+~- decay . C o r r e c t i n g t h e s e n u m b e r s fo r the above m e n t i o n e d e f f e c t s we ob ta in the fo l l ow-

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trig ratio:

p = (I~s" ~+~-)/(K°total) = 0.345 ± 0.005.

Assuming TCP invariance 3) and that all neutral I~s decays are ~o~o we get our value:

R = (K° ~ + ~ - ) / ( K ° - ~ ° ~ ° ) = 2.22 ± 0.I0.

In o r d e r to l ook f o r s o m e p o s s i b l e b i a s e s s o m e 2.4 c o n s i s t e n c y c h e c k s w e r e m a d e . R

2.0 T h e v a l u e s of R f o r d i f f e r e n t r e g i o n s of t he

i n t e r a c t i o n p o i n t a r e g i v e n in T a b l e 1. T h e v a r - i a t i o n of R w i t h t he K ° m o m e n t u m , K ° dip, (K ° , K -+) a n g l e , w i t h t he p r o t o n a n d ~+ m o m e n t a a n d w i t h t he p r o b a b i l i t y of t h e 1C f i t w a s s t u d i e d ( f i g . l ) . No s i g n i f i c a n t e f f e c t c o u l d b e s e e n . 2 .4

R Table I 2 . 0

Values of R when dividing the interaction volume in two along each coordinate axis.

X Y Z R 2.21 + 0.14 2.32 + 0.16 2.21 + 0.14

2.23 + 0.14 2.11 + 0.13 2.23 + 0.15

T h e c o n t a m i n a t i o n of o u r two p r o n g s a m p l e by o t h e r h y p o t h e s i s w a s e x a m i n e d . A s a f e t y cu t in t h e c o p l a n a r i t y ( -0 .02<coso¢<0.02) w a s m a d e f r o m the b e g i n n i n g o n a l l e v e n t s to e l i m i n a t e a p o s s i b l e c o n t a m i n a t i o n f r o m e l a s t i c e v e n t s . T h e v a l u e of the r a t i o w a s c a l c u l a t e d t a k i n g on ly t h e e v e n t s f o r w h i c h one of t h e m i s s i n g m a s s e s f o r r e a c t i o n (2) o r (4) w a s c o m p a t i b l e w i t h i n o u r e x - p e r i m e n t a l r e s o l u t i o n 4 ) . We o b t a i n R 1 = 2 .32 + 0 .19. T h e r e s t of o u r s a m p l e g i v e s R 2 = 2 .17 ± 0 .12 . T h e two v a l u e s a r e qu i t e c o m p a t i b l e , f u r - t h e r m o r e a c o n t a m i n a t i o n in t he two p r o n g topo logy would h a v e l ed to R 2 > R 1.

T h e K ° l i f e t i m e u s e d in t he w e i g h t i n g f a c t o r w a s t he w o r l d a v e r a g e v a l u e [1]. If we h a d u s e d t h e v a l u e we f ind f r o m o u r s a m p l e T s = (0.93 ± 0 .03) × 10 -10 s e c , t h e v a l u e of R would be 2 .23 s h o w i n g t ha t t he s h i f t i s n e g l i g i b l e wi th r e s p e c t to the s t a t i s t i c a l e r r o r .

O u r r e s u l t h a s to b e c o m p a r e d w i t h o t h e r e x p e r i m e n t s . U n t i l 1969 t h i s r a t i o w a s p o o r l y k n o w n [2]. T h r e e e x p e r i m e n t s a p p e a r e d t h e n [ 3 - 5 ] , m e a s u r i n g t he v a l u e of R by d e t e c t i o n of

3) Under T C P invari~nce we have K~s ~ ~K~otal(1-2 Re~) where 2 R e E ~ ( K s | K L > ~ 3 . 2 7 x 10-o [1].

4) These events have been re ta ined in our sample as un- ambiguous e i t he r by an ionization decis ion or because of a fi t fa i lure . The mis s ing m a s s in te rva l s used for react iotm (2) ~n~ (4) were respec t ive ly 0.0 < (MM~.) 2 < 0.04 (GeV/c~) ~ and 0.82 < (MM4) 2 < 0.94 (GeV/c2) 2 cor responding to about twice the exper imenta l re~ol- ution.

2 . 4 R

2 . 0

2 . 4 R

2 . 0

2 . 4 R 2 . 0

2.,! 2 . 0

R = 2 . 2 2

R v s . K ° M O M E N T U M

2o0 , 6,o0 , 1o9o

1 I

R vs. S I N ( D I P K ° ) I

~ vs. C~(K.*K °) 0 1 I I 1

. ( . ° v/~ ) I

Y ~ " ~ J J J ~ J J J J J J J J J J J J J J J . . . . ~

T t R vs. P M O M E N T U M

2po , 6100 , 1000 p (MeV/c),

R vs. n'÷ M O M E N T U M

2 ~ 6qo I [

1ooo p~u,v/c)

R vs. P()C 2) 0 1 I I I

Fig.1. Variation of R with the K ° momentum, sin(DIP K°), K ° lab. production angle, proton and ;r + momenta, prob- ability of the 1C fit. The hatched band corresponds to R = 2.22 + 0.10 and extends over the experimental range

of the variables.

the neutrals. Very recently another hydrogen

bubble chamber experiment [6] based on the same

principle as ours (i.e. without direct detection Of K~s--. ~°~°) a n d w i th i n c i d e n t K - , g a v e R = 2.22 ± 0 .095 and a w o r l d a v e r a g e v a l u e R = 2 .225 ± 0 .03. T h e i m p r o v e m e n t in t he e x p e r i m e n t a l s i t u a t i o n fo r t he v a l u e of R g i v e s a s i g n i f i c a n t d e v i a t i o n f r o m 2.0. T h i s d e v i a t i o n c a n b e due to d i f f e r e n c e s in p h a s e s p a c e , to r a d i a t i v e c o r r e c t i o n s and to

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Volume 39B, n u m b e r 4 P H Y S 1 C S L E T T E 15 May 1972

p o s s i b l e A1 > ~ t r a n s i t i o n s . W u a n d Y a n g [7] p o i n t e d o u t t h a t t h e m e a s u r e -

m e n [ of R i s t h e o n l y p o s s i b l e d i r e c t m e a s u r e - m e n t of Re(A2/A o) w h e r e A 2 a n d A o a r e t h e 1 = 2 a n d l = 0 t w o - p i o n a m p l i t u d e s . O n e h a s [8]:

R - 2 = 6 J - 2 R e (A2/A o) c o s (5 2 - 5 0 ) +

w h e r e 5 o , 5 2 a r e t h e p h a s e s h i f t s in t h e I = 0 a n d I = 2 ~ s t a t e s , a i s t h e r a d i a t i v e c o r r e c t i o n i n c l u d i n g t h e p h a s e s p a c e c o r r e c t i o n [ 8 - 1 0 ] . W e wi l l u s e in t h e f o l l o w i n g c~ = 0 ± 0 . 0 4 b ) .

T a k i n g 52 - 5o = - 3 4 0 + 8 ° a s m e a s u r e d in ;;~ i n t e r a c t i o n s [11] we o b t a i n R e (A2/A o) = 0 .031 + 0 . 0 1 5 . U s i n g t h e w o r l d a v e r a g e v a l u e o f R , t h e e r r o r i s r e d u c e d to 0 . 0 0 8 s h o w i n g a c l e a r e v t - d e n c e f o r t h e v i o l a t i o n of t h e A I = ½ r u l e . A t t h i s

o) The t h r ee ca l cu la t ed v a l u e s for o~ a r e 0.04 + 0.04 [9], 0 .006[10] , -0 .006111] . The r ad ia t ive and phase space c o r r e c t i o n s a r e of oppos i t e s i g n s . C o r r e c t i o n for rea l y ' s with a m o m e n t u m lower than 10 MeV i s a l so inc luded .

In the s a m e e x p o s u r e the th ree body K o decay was e x t e n s i v e l y s tud ied with ten t i m e s m o r e p i c t u r e s [ 1 2 ] . It t u r n s out tha t the e x p e r i m e n t a l n u m b e r of yTry de - c a y s w i t h 7 ' s > 10 MeV is c o m p l e t e l y exp la ined by the b r e m s s t r a h l u n g e f fec t and t h e r e f o r e no f u r t h e r c o r r e c t i o n i s needed for our K ° ~ y+ ~: s a m p l e .

l e v e l h o w e v e r o n e s h o u l d n o t i c e t h a t t h e s t a t i s - t i c a l e r r o r o n R i s o f t h e s a m e o r d e r a s t h e e r r o r on t h e e v a l u a t e d c o r r e c t i n g f a c t o r ~ .

[7]

[8]

[9]

[10]

[11]

[12]

References [1] P a r t i c l e Data Group , Rev. Mod. P h y s . 4 3 (1971)S1. [2] B. Auber t , Topica l Confe rence on Weak i n t e r a c t i o n s

Geneva 1969, Repo r t CERN 69-7 , p. 205. [3] B. Gobbi, D. Green , W. Hake[, R. Moffet t and

J . Rosen , k h y s . Rev. L e t t e r s 22 (1969) 682. [4] J . G . M o r f i n a n d D. S inc la i r , P h y s . Rev. L e t t e r s 23

(1969) 660. [5] G. Bozoki , E . F e n y v e s , E . G o m b o s i , E. Nagy,

G. Suranyi , F . T ~lbisz, and G. V e s z t e r g o m b i , Phys . L e t t e r s 30B (1969) 498.

[6] C. Ba[tay, A. B r i d g e w a t e r , W . A . Cooper , L . K . G e r s h w i n , M. Habibi and N. Yeh, P h y s . Rev . L e t t e r s 27 (1971) 1678. Ta t T s u n Wu and C. N. Yang, P h y s . Rev. L e t t e r s 13 (1964) 380. F. Abbud, B . W . Lee and C .N. Yang, Phys . Rev. L e t t e r s 18 (1967) 980. A. A. Belavin and I. M. N a r o d e t s k y , I hys . L e t t e r s 26B (1968) 668. O. N a c h t m a n n and E . d e Rafae l , CERN, Repo r t TH 1031, Unpub l i shed . J . P. Baton, G. L a u r e n s and J . R e i g n i e r , P h y s . L e t t e r s 33B (1970} 528. G. Bu rgun , T h e s i s , r a p p o r t CEA, to be pub l i shed .

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